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Teachers' Manual 



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Andrews' Lunar Tellurian 



BY 



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HOWARD H. GROSS. 



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Published by 

A. H. Andrews & Co., 

Chicago. 

1881. 



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Copyrighted by 

Howard H. Gross, 



Chicago, 1S81 . 



Introduction. 



To The Teacher: 

In the preparation of this Manual the writer has endeavored to 
treat the subjects presented 'in a simple yet forcible manner, 
avoiding, as much as possible, technical terms. The illustrations 
given, outline the work that should be done in the class-room. 
The teacher should, and no doubt will supplement these illustra- 
tions in many ways, presenting the subjects treated step by step, 
in a thorough and yet attractive manner. 

The value of demonstration is no longer doubted, and in those 
schools where it is most used the best results follow. This is 
preeminently true in geographical and astronomical work. The 
Lunar Tellurian is designed to furnish the illustrations necessary 
to give the pupils a comprehensive understanding of the relation- 
ships of the earth, sun and moon. It is so simple in construc- 
tion that the average teacher may use it to advantage after a few 
hours' study with the Manual, 

The teacher will find it advantageous to now and then assign a 
topic to one of the pupils, and require him to furnish clear and 
forcible demonstrations by use of the apparatus. 

The teacher's attention is particularly called to the section in 
which Prof. E. Colbert, now scientific editor of the Chicago 
Tribune, and well known as a practical astronomer, treats the sub- 
ject of Tides. His presentation is new, having reduced the ab- 
stract to the concrete. The author congratulates the readers upon 
being able to present an article from the pen of Prof. Colbert, and 
here acknowledges obligations to that estimable and scholarly 
gentleman. 

The writer acknowledges his obligations to M. MacVicar, Ph. 
D., of the Michigan State Normal School — than whom there is 
no better authority on mathematical geography — some of whose 
illustrations the writer has embodied in this work. 

Chicago, March i, 1881. 




Andrews' Lunar Tellurian. 




A. The globe ball. S. Arc of the sun's circumference, drawn 
upon the same scale as the globe. Extend the arc S until a circle 
is completed, and this circle shows the size of sun upon the same 
scale as the globe represents the earth. B. The circle of 
illumination, showing how far the sunlight extends. C. The twi- 
light circle showing how far the twilight extends. D. The moon 
ball, showing the light and dark hemispheres of the moon. The 
gearing at F keeps the light hemisphere always toward the sun. 
E. Plate showing the inclination of the moon's orbit. G. A cal- 
endar index. L. Pointer showing the position of the sun's verti- 
cal ray. H. A longitudinal or time index, used to find time of 
sunrise and sunset, length of days, nights and twilight. J. The 
ecliptic. K. The equator. 



6 Lunar Tellurian Manual. 

To adjust the Lunar Tellurian. 

To adjust the apparatus to agree with the calendar 
move the arm IX until the calendar index G is opposite the 
21st of June ; place the arm in which the south pole of the 
globe is fastened parallel with the arm IX as shown in 
cut, or bring the calendar index to June 21st and place 
the centre of the socket at the south pole opposite the 
mark I on the semi-circular brace joining the ends of 
circle C. The pointer L should be parallel with the 
arm IX. 

Raise the moon ball until the gear wheels at F are 
disengaged, turn the cog wheel to the right or left until 
the white side of the moon ball is toward the sun, drop 
the cogs into gear. The gearing will keep the bright 
side of the moon ball towards the arc S. 

The apparatus is now fully adjusted for use. 

PREPARATORY WORK. 

The study of the method of adjusting and handling 
the Lunar Tellurian Globe in illustrating and solv- 
ing problem. 

Before using the globe in illustrations, the following 
points should be carefully studied. Each adjustment 
should be made familiar by actual practice. The teacher 
cannot be too particular on this point, as the power of 
any illustration depends largely upon the tact with which 
the piece of apparatus used is handled. 

The cut upon the preceding page represents the globe 
with all the attachments in position. Let every part be 
removed and replaced and set in the positions indicated 
again and again, until every thing required can be done 
with ease and rapidity. 



Lunar Tellurian Manual. 7 

Be particular to notice the following suggestions : 

1. The arc 6* represents the curvature of the surface of 
a ball which bears the same relation in size to the sun 
that the globe A bears to the earth. Hence, by com- 
pleting the circle of which the arc 6 1 is a part, and com- 
paring it with a great circle on the globe, we have a cor- 
rect representation of the relative size of the earth and 
sun. 

2. The pointer L represents a line connecting the 
centre of the earth and sun, hence, indicates the position 
of the only vertical ray of light or heat which comes 
from the sun to the earth. 

3. The circle B is used to indicate the line which sep- 
arates light from darkness; hence is called the "Circle of 
Illumination," or " Day and Night Circle." 

General Definitions. 

The following definitions should be made familiar be- 
fore commencing the use of the globe : 

1. A Point is that which has position without mag- 
nitude. 

2. A Line is the path of a moving point. 

3. A Straight Line is one which has the same di- 
rection throughout its entire length. 

4. A Curved Line is one which changes its direc- 
tion at every point. 

5. Parallel Lines are lines which have the same 
direction. 

6. An Angle is the opening between two lines which 
meet in a common point called a vertex. 



s 



Lunar Tellurian Manual. 



There are three kinds of angles, thus 



(1) 



(2) 

B 
— ^^ 



(31 



(4) 



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HORIZONTAL. /» 4 

Tuo Right Angles, One Eight Angle. Obtuse Angle. Acute Angle. 

7. When a line meets another line, making, as is 
shown (in 1"), two equal angles, each angle is a Rigllt 
An gift, and the lines are said to be perpendicular to each 
other. 

8. An Obtuse Angle is an angle (as shown in 6— 
3), that is greater than a right angle. 

9. An Acute Angle is an angle (as shown in 6 — 
4). that is. less than a right angle. 

10. A Plane is a surface traced by a straight line 
moving in the same direction. 

11. A Circle is a sur- 
face enclosed by a curved 
line, every point of which is 
equally distant from a point 
within called the centre. 

1 2. A Circumference 

is the line that bounds the 
circle. 

In describing the lines on 
the surface of the globe, the 
word circle is used in place of circumference. When a 
circle proper is intended, the word ,; plane' r is introduced. 

13. A Degree is one of the 360 equal parts into 
which the cir conference of a circle is supposed to be 
divided. 




dS &nL Circle- 



Lunar Tellurian Manual. 



Observe the length of a degree varies with the size of 
the circle. 

14. The Diameter of a circle is a straight line pass- 
ing through its centre and terminating at both ends in 
the circumference. 

15. The Radius of a circle is any straight line ex- 
tending from its centre to the circumference, 

16. A Sphere is a solid or volume bounded by a 
curved surface, such that all points in it are equally dis- 
tant from a point within called the centre 

Observe the point e, in the 
cut in the margin, is the centre •* 9^ 
of a sphere of which cbd is the 
lower half. 

17. The Diameter of a 

sphere is a straight line passing 
through its centre and termin- 
ating at both ends in the surface. 

In the cut ab and cd are di- 
ameters. 

18. The Radius of a sphere is a straight line drawn 
from the centre to any point in the surface. 

In the cut, ce,fe, ae^ ge and de are radii. 

19. A Great Circle of a sphere is one whose plane 
passes through the centre of the sphere. 

Hence the planes of all great circles divide the sphere 
into two equal parts. Each part is called a Hemisphere. 

20. A Small Circle of a sphere is one whose plane 
does not pass through the centre of the sphere. 




io Lunar Tellurian Manual. 

♦ Hence, the planes of all small circles on a sphere di- 
vide the sphere into two unequal parts. 

21. The Axis of the Earth is that diameter on 
which it rotates once in twenty-four hours. 

22. The Poles of the Earth are the two points on 
its surface at the extremities of its axis. 

23. The North Pole is the Pole directed to the 
North Star. The South Pole is the opposite extrem- 
ity of the axis. 

24. The Equator is a great circle midway between 
the poles whose plane is at right angles to the axis of the 
earth. 

25. The Parallels of Latitude are small circles 
parallel to the Equator. 

26. A Meridian is a semi-circle extending from 
Pole to Pole. 

27. The Latitude of a place is its distance in degrees 
north or south of the Equator. 

Places north of the Equator are said to be in North 
Latitude, and places south in South Latitude. 

28. The Longitude of a place is its distance in de- 
gress east or west of a given meridian called the First 
or Prime Meridian. 

The meridian of the Royal Observatory at Greenwich, 
England, is commonly employed as the Prime Merid- 
ian. The French use the meridian of Paris; the Ger- 
mans that of Ferro, one of the Canary Islands; and 
Americans frequently use that of Washington. 

29. The Tropic of Cancer is a parallel of latitude 
23^ degrees north of the Equator. 



Lunar Tellurian Manual. ii 

30. The Tropic of Capricorn is a parallel of lat- 
itude 23^- degrees south of the Equator. 

31. The Orbit of the Earth is the path in which it 
moves round the sun. 

Observe, the flane of the earth's orbit is the plane in 
which the orbit is described. 

32. The Zones are broad belts or divisions of the 
earth's surface bounded by the Tropics and Polar Circles. 

These four lines divide the surface of the earth into five 
zones or belts known as the Torrid Zone, the two Tem- 
perate Zones, and the two Frigid Zones. 

The width of the Zones depends entirely upon the in- 
clination of the axis. The width of the Torrid Zone is 
double the inclination of the axis (23-J- degrees), or 47 de- 
grees. The width of the Frigid Zone is equal to the incli- 
nation. The Temperate Zones embrace whatever surface 
lies between the Tropics and Polar Circles (43 degrees). 
If the inclination of the axis were 30 degrees, as in the 
case of the planet Saturn, the Zones would be as follows : 
Torrid Zone, double the inclination, 30° or 60° 

Frigid Zones, each equal to the inclination, 30° or 60° 
Temp. Zones, each equal to the inclination, 30° or 60° 

Total degrees from pole to pole, - - 180° 

33. The Ecliptic is the sun's apparent yearly path 
through the fixed stars, or the earths real path or orbit. 

34. The Zodiac is a belt of the heavens 16 degrees 
wide, lying 8 degrees on each side of the Ecliptic, within 
which the sun, moon and planets are seen to move. 

This belt is divided into twelve equal parts called 
Signs of the Zodiac. These divisions, with their names, 
are represented on the base of the Lunar Tellurian. 



12 Luxar Tellurian Manual. 

35. The Equinoctial or Celestial Equator Js 

a. great circle of the Celestial Sphere directly over the 
terrestrial equator ', and hence is in the same plane. 

36. The Equinoctial Points or Equinoxes 

are the points where the Ecliptic crosses the Equinoctial. 

The points which the sun passes in March is called the 
^'ernal Equinox, and that which he passes in September 
the Autumnal Equinox. 

37. The Solstitial Points or Solstices -^re the 

two points where the Sun is farthest from the Equinoc- 
tial. 

The point north of the Equinoctial is called the Sum- 
mer Solstice^ and the one south the Winter Solstice. 

38. The Declination of a heavenly body is its dis- 
tance north or south from the Equinoctial. 

Declination corresponds to terrestrial latitude. 

39. Perihelion is the point in the earth's orbit 
nearest to the sun. 

40- Aplielion is the point in the earth's orbit far- 
thest from the sun. 

41. Refraction in Astronomy is the change of di- 
rection which the rays of light undergo in passing through 
the atmospheir. 

This may be illustrated to a class by placing on the 
blackboard a diagram; thus. 



Lunar Tellurian Manual. 



13 




F E E F 

Let vS represent the sun, D the earth, and F and E 
two strata of the atmosphere of which E is the more 
dense. 

Ask the pupil to observe, 

(a) That if a ray of light from 6* enter the stratum F 
at 3_, it will be bent toward the perpendicular 3b 5 and 
enter the stratum E at 2. The stratum E being more 
dense than the stratum F, it is again bent towards the 
perpendicular 2a^ and strikes the surface of the earth at 1. 

(<5) That the atmosphere is not made up, as represented 
in the diagram, of separate strata of different densities, 
but becomes gradually more dense the nearer it is to the 
surface of the earth. Hence the rays of light in passing 
through the atmosphere curve gradually toward a per- 
pendicular to the surface of the earth from the point 
where they enter the atmosphere. 

(c) That there is no refraction when a ray of light 
strikes the atmosphere perpendicularly, as shown by the 
line lZj and that the more obliquely a ray enters, the 
greater the refraction, as shown by the line 1 3S. Hence, 



14 Lunar Tellurian Manual. 

light coming from any heavenly body in our zenith, un- 
dergoes no refraction, and as a body moves from the 
zenith to the horizon, the refraction increases. 

(d) That since all objects are seen in the direction in 
which the light from them falls upon the retina of the 
eye, the sun S in the diagram is seen by an observer at 
1 in the direction of SI. In consequence of this effect 
of refraction no heavenly body, unless in the zenith, is 
seen in its real position. 

In the case of the sun and moon, the amount of refrac- 
tion at the horizon is a little greater than their apparent 
diameters. Hence, in rising or setting, they appear 
above the horizon when they are actually below it. 

42. The Radiation of heat with reference to the 
earth is the emission and diffusion of heat from its surface 
into the atmosphere. 

Ask the pupils to observe, 

(a) That during the day the surface of the earth is 
heated by the rays of the sun. 

(b) That when the sun sets the earth radiates its heat 
into the atmosphere; hence the change in the tempera- 
ture before the sun rises. 

In the summer season the earth's surface absorbs or 
takes in more heat from the sun during the long day than 
it radiates or gives out during the short night, the tem- 
perature must for this reason rise. When the sun leaves 
us and goes south our days shorten and nights lengthen, 
during which absorption diminishes, radiation increases, 
and the temperature is correspondingly lowered. 

The blacksmith puts the horseshoe into the forge that 
it may absorb heat until it gets soft, so that he can easily 



Lunar Tellurian Manual. 



IS 



shape it upon the anvil; while working with it the shoe 
radiates heat, getting thereby more and more difficult to 
work and soon must be replaced in the forge to again 
absorb the required quantity of heat to be easily and 
economically worked, when the smith is through with 
the shoe he drops it into his tub of water that it may quickly 
radiate the heat and be ready to nail to the horse's hoof. 

Distribution of Light and Heat. 

To illustrate the difference between the sun's ver- 
tical and oblique rays* 

Take two pieces of cardboard about a foot square. In 
the centre of one of them cut a round hole about one inch 
in diameter; hold this one up to the sun at a right angle 
to the rays, so that the light will pass through the open- 
ing; place the other piece about a foot behind the first 
and parallel to it; ask the pupils to observe that the sun- 
light passing through the inch opening falls upon the 
second piece vertical to it, and covers alike surface of one 
inch. This illustrates how the sunlight, falling verti- 
cally upon the earth, covers a surface equal to the volume 
of such light. 

Change the position of the back piece of cardboard 
slowly, so that it will not be parallel to the first, and ask 
the pupils to observe that while no more sunlight passes 
through the opening in the first cardboard than in the 
other illustration, yet that amount is spread over a greater 
surface on the second piece, owing entirely to the fact 
that it now falls obliquely / whereas, in the first instance, 
it fell vertical to the surface of the cardboard. This illus- 
trates how the sunlight, falling obliquely upon the earth's 
surface, covers a space greater in area than the volume 
of the light. Observe also that the greater the obliq- 
uity, the greater the space covered. 



1 6 Lunar Tellurian Manual. 

Remove the second piece of cardboard, and put the 
globe in its place in such a manner that the sunlight ad- 
mitted through the first cardboard shall fall vertical to 
the surface upon the equator. Observe that the area of 
light on the surface of the globe is about equal to the area 
of the hole admitting the light. Raise the cardboard so 
that the sunlight will fall upon the 40th parallel of north 
latitude, and observe that while no more sunlight is ad- 
mitted, it covers a much greater area, and must be less 
intense there than on the equator where the sun was 
vertical. In the same manner place the sunlight on the 
60th parallel, and observe the greater obliquity and the 
greater area covered. Call special attention to the fact 
that the curvature of the globe is the only cause of the 
rays in the higher latitude being more oblique than they 
are in the lower latitudes. 

Observe, that what is true of a small globe and a por- 
tion of sunlight, is true of our earth as a sphere, and 
the great volume of sunlight. 

Thus we find — 

1. That the nearer the vertical sun, the more intense 
the light and heat; and the farther from the vertical sun, 
the less intense the light and heat. 

Note. — If convenient, place a convex lens over the aperture in 
the cardboard ; place the second board behind, as directed in the 
first instance and at such a distance as necessary to make the 
converging rays cover the least possible surface ; hold the sunlight 
upon the same point for a few moments ; and if the lens is a good 
one combustion will ensue at the point of contact thus illustrating 
the intense heat produced by reducing the space covered by a 
given portion of sunlight. The intensity of solar heat is inversely 
proportional to the space covered by a given volume. 



Lunar Tellurian Manual. 17 

2. That only one- half o£ the earth's surface can, at any 
time, be exposed to the sun's light and heat. This half 
is called the Illuminated Hemisphere, 

Rotate the globe on its axis from west to east 10 de- 
grees, and ask the pupils to observe, in case the earth 
moves in like manner: 

(a) That a distribution of light and heat will have 
taken place. 

(b) That the vertical rays of the sun will have been 
carried westward 10 degrees upon the earth's surface, 
owing to this rotation to the east/ or, the sun's vertical 
ray will have been distributed east and west 10 degrees. 

(c) That the boundary of sun's light and heat will have 
been carried westward from 90 degrees west longitude to 
100 degrees, and that all places situated between these 
meridians will have been by this distribution brought into 
the illuminated hemisphere, while those places situated 
between the 90th and 80th meridians east longitude will 
have been carried out of it. 

{d) That the Day and Night Circle is parallel with 
the meridians as they pass under it. 

Rotate the globe once upon its axis from west to east, 
and ask the pupils to observe: 

(a) That by reason of this rotation the sun has crossed 
every meridian and returned to the place of starting. 

(b) That every meridian has passed through the illu- 
minated and the dark hemispheres. Hence, one com- 
plete distribution of light and heat east and west has taken 
place, being produced by the rotation of the earth upon 
its axis. As the earth turns once upon its axis daily, 
there must occur a daily distribution of light and heat 
east and west uj>on the earth? s surface. 



I - LfXAR I ILLCRTAX MaXTAL. 

(c) That when the sun is vertical to the equator, as on 
March 20th and September 23d, the light and heat of the 
sun is equally distributed in the north and south hemi- 

sphere=. 

To illustrate the distribution of light and. heat on 
March 20th. 

To produce a distribution of the sun's light and heat 

ur:::: ::~_e ear:h*5 surface. the ear:;; :r su:: :::us: chang-e 
their position in respect to the other. This necessitates 
a movement^ and without a movement no distribution 
can take place. 

It is very necessary that the pupils get a clear concep- 
tion of this subject and master it, as upon the distribution 
of light and heat depend the succession of day and night, 
the twilights, change of seasons, and, in fact, our very 
existence. 

Bring the calendar index to the 20th of March; rotate 
the globe upon its axis until the sun is vertical to the 
prime meridian, and ask the pupils to observe: 

(a) That the sun is vertical to the equator. 

{£) That the sun's light and heat extends north and 
south from pole to pole, as shown by the Day and Might 

Circ'.e 3. 

(c) That the sun's light and heat extends east and 
west of the prime meridian 90 degress, as shown by the 

;:.:.;.- ar.i r.ig::: ::rc~e 3. 

To illustrate the distribution of light and heat on 
the 21st of June. 

Bring the calendar index to the 21st of June, and ask 
the pupils to observe: 



Lunar Tellurian Manual. 19 

(a) That the sun is vertical to the Tropic of Cancer, 
23-J- degrees north of the equator. 

(B) That the Illuminated Hemisphere now extends 23-J- 
degrees beyond the north pole, and that it fails to reach 
the south pole by the same number of degrees. 

(c) That the place upon the earth's surface where the 
vertical ray falls, is the center of the Illuminated ^Hemi- 
sphere, and that any change in position of this point pro- 
duces a like change in the Illuminated, and an opposite 
change in the Dark Hemispheres. 

(d) That on June 21st the light and heat of the sun is 
unequally distributed in the north and south hemispheres ; 
that the Illuminated Hemisphere predominates north of 
the equator, and the Dark Hemisphere predominates 
south of it. 

Rotate the globe upon its axis, and ask the pupils to 
observe : 

(a) That the vertical sun traces the Tropic of Cancer. 

(&) That as the earth rotates upon its axis, in this man- 
ner, all places within the Arctic circle will remain in 
sunlight, while corresponding places within the Antarctic 
will remain without sunlight. 

(c) That from the 20th of March to the 21st of June, 
the vertical sun has been carried north 23|- degrees, or 
that a north and south distribution to the extent of 23|- 
degrees has taken place. 

To illustrate the distribution of light and heat on 
the 23d of September. 

Bring the calendar index to the 23d of September; 
this illustrates the relationship that exists between the 
earth and sun on that day. Ask the pupils to observe: 



20 Lunar Tellurian Manual. 

(a) That the vertical sun has. from the 21st of June 
to the 23d of September, been carried south from the 
Tropic of Cancer to the equator; and that the Illumin- 
ated Hemisphere has been correspondingly changed, so 
that on September 23d, the sun's light and heat is again 
equally distributed in the north and south hemispheres, 
and extending from pole to pole, as on March 20th. 

(b) That whatever distribution was shown, or what- 
ever observations could be made on March 20th, are again 
reproduced on September 23d. 

To illustrate the distribution of light and heat on 
December 22d. 

Bring the calendar index to the 22d of December, and 
ask the pupils to observe: 

(a) That the sun is vertical 2^/2 degrees south of the 
equator. 

[#) That the Illuminated Hemisphere now extends 
2 3/2 degrees beyond the south pole, and that it fails to 
reach the north pole by the same number of degrees. 

(c) That, on December 22d, the light and heat of the 
sun is again unequally distributed in the north and south 
hemispheres, and that the Illuminated Hemisphere pre- 
dominates south of the equator, and the Dark Hemi- 
sphere predominates north of it. 

Rotate the globe upon its axis, and ask the pupils to 
observe : 

(a) That the vertical sun traces the Tropic of Capri- 
corn. 

(b) That as the earth rotates upon its axis in this 
manner, all places within the Antarctic circle remain in 



Lunar Tellurian Manual. 21 

sunlight, while corresponding places within the Arctic 
circle will remain without sunlight. 

(c) That from the 23d of September to the 22d of 
December the Vertical sun has been carried south 23^ 
degrees, or that a north and south distribution has taken 
place. 

Bring the calendar index slowly to starting point 
(March 20th), and observe : That the vertical sun is 
carried from the Tropic of Capricorn to the equator, the 
place of beginning ; and that a north and south distribu- 
tion of the sun's light and heat has taken place from the 
equator to both tropics and return, and that the time 
necessary to do this is one year; and, as^the vertical ray 
is distributed, so must all other rays that touch the earth's 
surface be affected. 

Thus we see that there is a double distribution : east 
and west daily, and north and south annually. 

The causes of the existing distribution of light and 
heat* 

1. The Daily Distribution east and west is caused by 
the daily rotation of the earth on its axis. 

2. The Annual Distribution north and south is caused : 

(a) By the revolution of the earth in its orbit around the 
sun. If the earth remained fixed in its orbit, and re- 
volved upon its axis, but one distribution could take 
place — the daily. 

(b) By the inclination of the earth's axis. Notice that 
on the 20th of March the axis is inclined 23^ degrees, 
but that the inclination is neither to nor from the sun, 
and that the sun is then vertical to the equator. Notice 
that on the 21st of June the north pole is inclined to the 



22 Lunar Tellurian Manual. 

sun the full inclination of 23 ^degrees, and for this rea- 
son the sun is vertical the same number of degrees north 
of the equator. On December 22d, the north pole is in- 
clined from the sun the full inclination, this bringing 
Capricorn under the sun. Erect the axis by supporting 
the globe on the other socket, call the pupils' at- 
tention to the fact that the equator and ecliptic now lie 
in the same plane. Revolve the earth around the sun 
and observe that the vertical ray falls constantly upon 
the equator ; without an inclination no annual distribu- 
tion of light and heat could take place. 

(c) By the parallelism of the earth's axis. The axis is 
said to be parallel, because it points continually to the 
same part of the heavens : thus, the north pole points 
constantly towards the North Star, while the earth re- 
volves around the sun. Revolve the globe around the 
arc S and observe that the axis points constantly in the 
same direction. This is true of the earth and all the 
planets as they revolve in their several orbits. This is 
termed the parallelism of the axis. 

Equal Days and Nights. 

1. Bring the calendar index to the 20th of March, and 
ask the pupils to observe : 

(a) That the Day and Night Circle B divides the earth 
into two divisions — day and night: that all places on 
the side of this circle next to the sun have day, while 
those places upon the opposite side have night. 

(b) That at this season of the year the sun is vertical 
to the equator, and the Day and Night Circle is parallel 
to opposite meridians. 

(c) That in this position the Day and Night Circle 



Lunar Tellurian Manual. 23 

divides every parallel of latitude, from pole to pole, into 
two equal parts. 

Rotate the globe slowly upon its axis, and ask the 
pupils to observe : 

(a) That all places upon a given meridian enter the 
sunlight at the same moment. 

(b) That one-half a rotation on the axis carries these 
places through the Illuminated Hemisphere, where they 
pass beyond the Day and Night Circle, when the day 
ends and night begins. 

{c) That one-half a rotation carries these places from 
sunset to sunrise. 

Thus we see that on March 20th, the days and nights 
must be equal all over the earth's surface. 

Bring the calendar index to the 23d of September, and 
ask the pupils to notice that the same condition that ex- 
isted on March 20th, again exists, with the same result — 
equal days and nights. 

Unequal Days and Nights. 

Bring the calendar index to the 21st of June, and ask 
the pupils to^observe : 

(a) That the sun is vertical 23^ degrees north of the 
equator, and that the sunlight extends 231^ degrees be- 
yond the north pole, and fails to reach the south pole by 
the same number of degrees. 

(b) That the Day and Night Circle no longer divides 
the parallels of latitude into equal parts, but into two 
unequal parts ; and that north of the equator the greater 
part of every parallel is in the sunlight, and the lesser 



24 Lunar Tellurian Manual. 

part in darkness ; while south of the equator the lesser 
part is in sunlight, and the greater part in darkness. 

(c) That the entire parallels within 231^ degrees of 
the north pole are now in constant day, while those 
within the same distance of the south pole are in con- 
tinual night. 

Rotate the globe upon its axis, and ask the pupils to 
observe : 

(a) That no sunlight or day reaches that portion of 
the earth's surface within the Antarctic circle, although 
the earth may revolve upon its axis. 

(b) That the entire area of the earth's surface within 
the Arctic circle, is not carried out of the sunlight by 
the rotation of the earth upon its axis. 

(c) That the Day and Night Circle cuts the equator at 
opposite points, and that there the days and nights are 
equal. 

(d) That, as you proceed north from the equator to 
the Arctic circle, the days i?icrease in length gradually 
from 12 hours at the equator, to 24 hours within the 
Arctic Circle. 

(e) That, as you proceed south from the equator to the 
Antarctic circle, the days decrease in length gradually, 
from 12 hours at the equator, to hours within the Ant- 
arctic Circle. 

Bring the calendar index to the 22d of December, and 
ask the pupils to observe that what was true of the 
northern in June, is now true of the southern hemisphere 
in Dece??iber. Thus it is evident — 

1. That when the sun is upon the equator, the days 
and nights are everywhere equal. 



Lunar Tellurian Manual. 25 

2. That when the vertical sun is one or more degrees 
north or south of the equator, continual day must exist 
around the pole nearer the sun, and continual night must 
exist around the pole farther from the sun ; the extent 
of this area of continual day and night depending upon 
the distance of the vertical sun north or south of the 
equator. 

3. That the days and nights at the equator must al- 
ways be equal. 

4. That as you depart from the equator, the variation 
in the length of day and night increases, and as you ap- 
proach the equator the variation becomes less : the 
maximum variation being in the polar, and the minimum 
in the equatorial regions. 

5. That the length of any day upon any parallel of 
north latitude, is equal to the night following on the cor- 
responding parallel of south latitude. 

Note. — In this work we regard day as the time when the sun is 
present, and night as the time when he is absent. Night does not 
necessarily mean darkness. Night begins at sunset and ends at sun- 
rise. 

The Sun's Apparent JPath. 

Bring the calendar index to the 21st of June, rotate 
the globe on its axis until the Ecliptic marked upon the 
globe is brought under the vertical Sun. Move very 
slowly the calendar index through the succeeding 
months until it again comes to the 21st of June, and ask 
the pupils to notice that the vertical sun traces the 
ecliptic, and if the earth had no daily rotation on its 
axis, that the ecliptic would mark the true path of the 
Sun upon the earth. 

Rotate the earth upon its axis and ask the pupils to 



26 Lunar Tellurian Manual. 

observe that the sun traces the tropic of Ca?icer, and that 
if the sun should leave behind it a thread of light, that 
thread would lie upon the tropic. Move the calendar 
index to the 2 2d of June and rotate the globe upon its 
axis and notice that the sun traces a line parallel to the 
tropic of cancer, but about J^ of a degree south of it. 
In the same manner proceed with several days in succes- 
sion and observe that by reason of the rotation of the 
earth upon its axis and the movement forward of the 
earth in its orbit at the same time, the path of the 
vertical sun will be a continuous line running from east 
to west, and winding south from Cancer to Capricorn, 
and returning during the year, much as a thread is wound 
upon a spool. 

Change of Season. 

To produce what is called a change of season, at any 
place, more solar heat must fall upon that place during 
one part of the year than at another. Within the tropics 
the amount of heat received from the sun is nearly uni- 
form throughout the year, so that very little change of 
season takes place ; the greatest changes occurring in 
the higher latitudes. 

Bring the calendar index to the 20th of March and 
ask the pupils to observe : 

(a) That the light and heat of the sun are equally dis- 
tributed in the north and south Hemispheres. 

(b) That if the earth remained fixed in its orbit and 
was rotated upon its axis, there could be no change of 
seasons. 

Bring the calendar index to the 21st of June and ask 
the pupils to observe : 



Lunar Tellurian Manual. 27 

(a) That the sun is now vertical to the tropic of can- 
cer, and that the sun's light and heat is unequally dis- 
tributed in the north and south hemispheres, the north 
hemisphere having the greater, and the south hemisphere 
the lesser amount. 

(b) That owing to this inequality the north hemi- 
sphere is having its greatest amount of light and heat, its 
warmest season or Summer, and that the south hemi- 
sphere is having its coldest season or Winter. 

Bring the calendar index to the 23d of September and 
ask the pupils to observe that the light and heat is again 
equally distributed north and south of the equator as in 
March 20th. 

Bring the calendar index to the 22d of December and 
ask the pupils to observe that the sun is vertical to the 
tropic of Capricorn, the sun's light and heat being again 
unequally distributed in the north and south hemi- 
spheres, the south having the greater and the north the 
lesser amount ; and that at this time in the year the 
south hemisphere is having the warmest season or Sum- 
mer, while in the north it is in the coldest or Winter 
season. 

Bring the calendar index to the 20th of March, and 
observe that the sun is brought to the equator going 
north and that as it crosses, Spring begins in the north, 
and Autumn or Fall begins in the south hemisphere. 

The Causes that Produce the Changes of 

Seasons, 

The change of seasons is produced by, 

(a) The revolution of the earth in its orbit around the 
sun. 



28 Lunar Tellurian Manual, 

(b) The inclination of the earth's axis to the plane of 
the orbit. 

(c) The parallelism or fixed position of the earth's 
axis. 

(a 7 ) The rotation of the earth upon its axis. 

To illustrate that the rotation of the earth upon its 
axis is one of the causes that produce the changes of sea- 
sons as they now exist : Bring the calendar index to the 
20th of March, mark the point upon the equator where 
the sun is vertical at that time ; now move the calendar 
index slowly through the succeeding months of the year 
until it is again vertical to the same point. Call the 
pupil's attention to the fact that if the earth did not 
rotate upon its axis the sun would require one year to 
cross all the meridians once, and that in this case it 
would cross them from west to east instead of from east 
to west; that the sun would in that event rise in the west 
and set in the east, and our day and year would be of 
the same length ; and, that if this were true, the side of 
the earth towards the sun' would be parched by the ex- 
treme heat, while the opposite side would become frozen 
and lifeless. So, if the earth did not rotate on her axis, 
no changes of seasons as they now exist could take place, 
nor in fact could animal and vegetable life as now con- 
stituted endure the extremes of heat and cold to which 
they would be subjected. 

Twilights. 

To show how the sun after going below the horizon 
continues to give reflected light, and hence, produces twi- 
light. 

The molecules of which the atmosphere is composed, 



Lunae Tellurian Manual. 



29 



reflect the light they receive from the sun, and by the 
light so reflected, objects are seen in the absence of 
direct sunlight. The atmosphere is capable of thus 
reflecting light a mean distance of 18 degrees of a 
great circle. Call the pupils' attention to the fact 
that the sun gives direct light from the point where 
he is vertical to the Day and Night circle B and 
that the indirect or reflected light extends to the 
circle C, and that the space between these circles is called 
the Twilight Belt. Hence the earth's surface as regards 
light is divided into three sections : 1. A hemisphere of 
direct light. 2. A belt 18 degrees wide of reflected light 
or twilight. 3. The remaining portion without light. 

To illustrate the twilight on the 20th of March* 

Bring the calendar index to the 20th of March. Call 
the pupil's attention to the fact that there are two twi- 
lights Evening and Morning ; that the evening twilight 
deepens into darkness, while the morning twilight bright- 
ens into sunshine. Rotate the globe upon its axis and 
ask the pupils to observe : that places upon the earth's 
surface must cross the twilight belt twice in every 24 
hours. Rotate the globe slowly upon its axis and ask 
the pupils to observe: that all places upon thp same 
meridian from pole to pole pass into evening twilight at 
the same instant, but that those places located near the 
equator pass out of twilight first, and that the higher the 
latitude the longer the twilight continues. This varia- 
tion is due : 

i st. To the fact that at the equator the earth rotates 
faster than it does near the poles, for the same reason 
that the outer part of a wagon wheel turns faster when 
the wagon is in motion, than the hub. 



30 • Lunar Tellurian Manual. 

2d. This variation is partially due to the fact that 
places near the equator are carried across the twilight 
belt in a straight line, and at right angles to it : while 
near the poles places enter the twilight at right angles 
with the first circle and cross the belt not in a direct, line 
but travel on an arc of a circle passing obliquely across 
the second circle. 

From this we see that places in the higher latitudes 
must travel farther to cross the twilight belt, and at the 
same time, much slower than those places situated near 
the equator. 

Locate upon the map of the globe the place where 
you are situated, rotate the globe upon its axis and ask 
the pupils to note carefully the manner this place is car- 
ried across the twilight belt. This illustrates the twi- 
lights on the 20th of March, for that place. 

To illustrate the Tivilights on the 21st of June. 

Bring the calendar index to the 21st of June and ask 
the pupils to observe : 

(a) That the twilight belt no longer conforms to the 
meridians, and that no two places upon the same meri- 
dian enter the evening or emerge from the morning twi- 
light at the same moment. 

(6) Those places that in March cross the twilight belt 
at right angles to it, now cross it obliquely, so that the twi- 
lights for these places must be longer in June than in 
March. 

(c) That the obliquity is least at the equator, and in- 
creasing as the latitude increases. 

Locate upon the map of the globe the place where 
you are located, rotate the globe upon its axis and ask 



Lunar Tellurian Manual. 31 

the pupils to observe that this place is carried across the 
twilight belt more obliquely than in March and that the 
twilight must be of longer duration. 

To illustrate the Twilight on the 23d of September. 

Bring the calendar index to the 23d of September, ex- 
amine the twilight in the same manner as upon the 20th 
of March, and ask the pupils to notice that all the facts 
are the same as were observed at that date. 

To illustrate the Twilight on the 22 d of December. 

Bring the calendar index to the 22d of December, and 
ask the pupils to notice that places upon the earth's sur- 
face are carried across the twilight belt obliquely sub- 
stantially as in June. 

Compare the twilights of any place*, at different dates 
by use of the globe, taking the 21st of June as the basis 
of comparison, and repeat the comparison until the 
pupils see clearly, 

(a) That on the 21st of June the given place crosses 
the Twilight Belt more obliquely than on either of the 
other dates, and, hence, the longest twilight. 

(0) That on the 20th of March and 23d of September, 
the path of the given place across the Twilight Belt is 
the same, and less oblique than at either of the other 
dates, and hence the shortest twilight. 

(c) That on the 22d of December the given place 
crosses the Twilight Belt less obliquely than on the 21st 
of June, and more obliquely than on the 20th of March 
and 23d of September. Hence, a mean twilight between 
the other two. 

*The auther would suggest that the place selected be in north latitude 40 to 50 
degrees. 



32 Lunar Tellurian Manual. 

3. Now ask the pupils to notice that on the 226, of 
December the sun is vertical to south latitude 23^, and 
on the 21st of June north latitude 23^. Consequently 
the sun sustains the same relation in every particular to 
the Southern Hemisphere at the former date, that it does 
at the latter^date to the Northern. Hence, all the facts 
observed regarding the twilight on the 21st of June in 
northern latitudes apply on the 22d of December to cor- 
responding southern latitudes. Hence, all the facts 
observed on the 2 2d of December in northern latitudes 
may be found on the 21st of June in the southern 
latitudes. 

Sun's Declination. 

The Sun's Declination is his distance north or south 
of the equator (as indicated by the vertical ray). When 
the sun is north of the equator he is said to have a 
northern declination ; when south of the equator he is 
said to have a southern declination. 

The greatest northern declination (2$% degrees) oc- 
curs on the 21st of June, and the greatest southern de- 
clination (23^ degrees) occurs December 22d. At the 
time of the equinoxes (March 20 and September 23d,) the 
sun has no declination. 

To Find the Sun's Declination for any Day. 

Bring the calendar index to the given day, rotate the 
globe upon its axis until the meridian having the degrees 
upon it is brought under the pointer L. Extend the 
pointer L to the globe. The degree of latitude under 
the pointer is the required Declination. 

To find the Longitude of any place. 

Rotate the globe upon its axis until the given place is 



Lunar Tellurian Manual. 33 

under the pointer H, the degree on the equator at the 
end of the pointer H is the longitude required. The 
longitude is east or west according as the place is east or 
west of the Prime Meridan. 

Examples. 

1. What is the longitude of New York? 

2. What is the longitude of Calcutta? 

3. What is the longitude of Quito ? 

4. What is the longitude of St. Petersburg. 

5. What is the longitude of Honolulu? 

To find the Latitude of any place* 

Rotate the globe upon its axis until the given place is 
brought under the pointer H, above the place on the pointer 
read the degree of latitude required ; or, bring the given 
place under the edge of circle B, mark the circle directly- 
over the given place, rotate the globe until the meridian 
having the degrees marked upon it is brought under the 
circle. Under the point marked, read upon the meridian 
the degree of latitude required. If the place is north of 
the equator it is north latitude, if south of it south 

latitude. 

Examples. 

1. What is the latitude of New York ? 

2. What is the latitude of Calcutta? 

3. What is the latitude of Quito ? 

4. What is the latitude of St. Petersburg? 

5. What is the latitude of Honolulu? 

6. What is the latitude of Santiago ? 



LUNAR TELLURIAN MANUAL. 




Cut No. 2. 



Remove the day and night circle, as in the above cut. 
As now seen, the Lunar Tellurian should be used to 
explain the phases of the moon, eclipses, equation of 
time, precession of equinoxes, etc. 

34 



Lunar Tellurian Manual. 35 

Longitude and Time. 

Longitude is distance, measured, however, in degrees, 
minutes and seconds, east or west of a given meridian 
called the Prime Meridian. Observe that the degrees 
are marked upon the globe at the equator, east and west 
from the meridian of Greenwich — the prime meridian. 

On page (3) we learned that every circle is divided 
into 360 equal parts called degrees, every degree is sub- 
divided into 60 equal parts called minutes, and every 
minute is subdivided into 60 equal parts called seconds. 
The earth in its relation to the sun turns once on its 
axis (360 degrees) every 24 hours, and must turn as many 
degrees every hour as 24 is contained times in 360 or 15 
degrees. Since it turns 15 degrees in one hour, to turn 
one degree it will require jj of one hour or 4 minutes of 
time. 

Rotate the globe from west to east until the pointer L 
is over the prime meridian; noon now takes place upon 
that meridian from pole to pole. Observe that all places 
east of this meridian have passed the sun and that their 
noon has passed, while those places to the west have not 
yet been brought to the sun, and their noon will not yet 
have taken place. 

Example i. 

When it is noon (12 o'clock) at Greenwich, what is the 
time in Hamburg, say 10 degrees east of Greenwich? 
Hamburg being east of Greenwich the time is later by 
the time required by the earth to turn to degrees. Since 
the earth turns one degree in 4 minutes, to turn 10 
degrees will require 10 times 4 minutes or 40 minutes. 
The difference in time is therefore 40 minutes, and since 
it is 12 o'clock at Greenwich, it is 40 minutes after 12 at 
Hamburg, or 20 minutes to 1. p. m. 



36 Lunar Tellurian Manual. 

Example 2. 

When it is noon at Greenwich what is the time at Rio 
Janeiro, Brazil, 52 degrees west? 

Rio Janeiro being west the time is earlier by the time 
required by the earth to turn 52 degrees. Since the 
earth turns 1 degree in 4 minutes, to turn 52 degrees 
will require 52 times 4 minutes, or 208 minutes. Re- 
duced = 3 hours 28 minutes ; the time before noon at 
Rio Janeiro 12 o'clock noon less 3 h. 28 min. = 8 o'clock 
32 min. a. m. the time at Rio Janeiro. 

Example 3. 

When it is 1 1 o'clock a. m. at Hamburg what is the time 
at Charleston, S. C, 80 degrees west ? Charleston being 
west [the time is earlier. Charleston is 80 degrees west 
of Greenwich and Hamburg 10 degrees east, the dis- 
tance between Charleston and Hamburg is therefore 
80 degrees + 10 degrees = 90 degrees; 1 deg. = 4 min. 
90 deg. =90 X 4 = 360 minutes, reduced, = 6 hours. 
11 o'clock a. m., less 6 hrs. = 5 o'clock a. m. 

Example 4. 

When it is 10 o'clock a. m. at Constantinople, 28 de- 
grees east, what is the time at Hong Kong, 112 degrees 
east? Hong Kong being 112 degrees east and Constan- 
tinople being 28 degrees east, the distance between them 
;is 112 deg. less 28 deg. = 84 deg.; 1 deg. = 4 min.; 84 
-deg. = 84 X 4 = 336 min.; reduced F= 5 hrs. 36 min« 
difference in time. Hong Kong being east the time there 
is later than 10 o'clock a. m. by 5 hrs. 36 min. 10 hrs. -f- 
5 hrs. 36 min. = 15 hrs. 36 min. or as commonly read 
3 hrs. 36 min. p. m. 

Example 5. 

When it is 11.30 a. m. at San Francisco, 122 deg. west, 



Lunar Tellurian Manual. 37 

what is the time at Melbourne, Australia, 143 deg. east ? 
Ans. 5 hrs. 10 min. a. m. Observe that the greatest 
longitude a place can have is 180 deg., that is, half way 
around the earth from the prime meridian. If a person 
start at the prime meridian and go west he will be in 
west longitude until he reaches 180 degrees, when his 
longitude is either east or west. If he proceed on his 
course ten degrees, his longitude is 180 degrees east less 
10 degrees, or 170 East. If a companion had gone 10 
degrees east his longitude would be 180 degrees west less 
10 degrees, or 170 West; the men are manifestly 20 de- 
grees apart. 

To Find the Difference in Longitude Between two 

Places. 

1. If both places are in the same longitude either east 
or west, deduct the less from the greater and the result 
is their difference. 

2. If one place is east and the other west, the sum of 
their longitudes is the difference, provided the sum does 
not exceed 180 degrees. 

3. If one place is east and the other west, and the 
sum of their longitudes exceeds 180 degrees, deduct the 
amount from 360 degrees, and the remainder is the differ- 
erence of longitude sought. 

Suppose James and Howard leave the prime meridian, 
James going west and Howard going east ; when each 
has traveled 80 degrees they are 160 degrees apart, 
which is their difference in longitude, Howard being east 
of James. Let each proceed 10 degrees farther and 
they are 180 degrees apart, on opposite meridians, How- 
ard being either east or west of James. Let them con- 
tinue in their course 10 degrees; James is then 100 de- 



38 Lunar Tellurian Manual. 

grees west and Howard ioo degrees east. Together 
they have traveled 200 degrees, and as 360 degrees are 
all there is to travel, 360 — 200 = 160, the number of 
degrees between them, Howard being now 160 degrees 
west of James. 

Let us presume they started on their journey at noon, 
and that each carried accurate time pieces ; when they 
had traveled 15 degrees James would find his watch an 
hour too fast, and to correct it he must turn it back, 
while Howard's watch is found to be an hour too slow 
and must be set ahead. To keep the watches right these 
changes must be made constantly, James turning his 
watch back 4 minutes for every degree traveled, and 
Howard setting his ahead in the same proportion. When 
each has traveled 80 degrees as above, and it is noon at 
the prime meridian, James' watch shows 6 hrs. 40 min. 
A. m. (80 X 4 = 320 min. = 5 hrs. 20 min. subtracted 
from 12 noon = 6 hrs. 40 min. a. m.) and Howard's 
watch shows 5 hrs. 20 min. p. m. When each has trav- 
eled 90 degrees, James has 6 o'clock a. m. and Howard 
6 o'clock p. m. when it is noon at the prime meridian. 
When each has traveled 179 degrees, James' watch shows 
4 minutes a. m., and Howard's shows 1 1 hrs. 56 min. p. m. 
When they meet at 180 degrees their watches show the 
same hour, 12, midnight. James has gained 12 hours by 
setting his watch back, while Howard has lost 12 hours 
by setting his ahead. Though both watches indicate the 
same hour there is really a day's difference in their time. 
Were they quick-witted Hibernians, we might readily 
imagine them addressing each other somewhat like this : 
Hello ! faix, its to-day wid me, but it's yesterday with you. 
It's naither, sir, the other replies, It's to-day wid me and 
to-morrow wid you. 



Lunar Tellurian Manual. 39 

To Find the Time of Sunrise for any Vlace or any 

Day in the Year. 

Arrange the globe as shown in Cut No. 1. Bring the 
calendar index to the given day, rotate the globe upon 
its axis until the given place is under the western edge 
of the day and night circle ; place the time index H op- 
posite zero on the equator; tighten the screw to hold it 
firmly in position. Turn the globe upon its axis from 
west to east, until place mentioned is opposite the 
pointer L ; note on the equator the number of degrees 
of longitude that has passed under the pointer, reduce 
the longitude to time (as directed in Longitude and 
Time, page 35). The result is the time from sunrise to 
noon, which, subtracted from 12 o'clock noon, gives the 

hour of sunrise. 

Examples. 

1. What is the time of sunrise at Chicago, May 1 ? 

2. What is the time of sunrise at New Orleans, June 
30, 1881 ? ^ ^ m 

2. What is the time of sunrise at Melbourne, Janu- 
ary 10? 

To Find the Duration of Twilight for any Flaee 
on any Day in the Year. 

Arrange the globe as above. Bring the calendar in- 
dex to the given day, and the given place to the begin- 
ning of twilight. Set the index H opposite zero on the 
equator ; rotate the globe upon its axis until the given 
place is carried across the twilight belt; note the num- 
ber of degrees on the equator the globe has turned, 
which reduce to time and the result is the duration of 

twilight required. 

Examples. 

1. What is the length of twilight at San Francisco, 
August 1 ? 

2. What is the length of twilight at Berlin, June 21 ? 



40 Lunar Tellurian Manual. 

The Sun. 

The Sun is the centre of our solar system, and around 
him all the planets revolve and from him receive their 
light and heat. In matter he is 750 times greater than 
all the planets combined. As all bodies attract each 
other and in proportion to the amount of matter they 
contain, so the sun's attraction must be 750 times greater 
than the combined attraction of all the planets, and were 
they all to unite they could not move him his own dia- 
meter from the centre of gravity of our solar system. 
So we may justly regard the sun as the centre of gravity. 
The attraction of the sun is so much greater than 
the earth's, that a boy weighing 75 lbs. on the earth would 
weigh over a ton if placed upon the sun. 

The ancients thought the sun to be an immense globe 
of iron heated to a white heat. While this is not liter- 
ally true it shows they had a better idea of the sun than 
of the earth which they thought \dk>z flat. 

The apparent diameter of the sun is about y 2 a ^ e_ 
gree — rather more than less. When viewed through a 
powerful telescope his surface presents a mottled appear- 
ance, which Professor Xewcomb likens to a dish of rice 
soup with the rice grains floating upon the surface. 

The sun seems to be surrounded by a very rare, light 
atmosphere, principally hydr: gen heated to a glow, in 
which fleecv clouds seem to float; these clouds serve to 
cut off from us some of the fierce light and heat of the 
sun, and were it not for these, astronomers tell us his 
light and heat would be intolerable. 

The prevailing opinion of the best authorities is, that 
the sun proper is composed of condensed gasses under 



Lunar Tellurian Manual. 41 

great pressure, and heated to a temperature many times 
greater than furnace heat. 

The solar spectrum shows the presence of hydrogen, 
iron, magnesium, sodium and other elements in the sun ; 
but of what the sun is composed we know very little. 
His extreme brightness renders observations very diffi- 
cult. If the sun were placed at the distance of the 
nearest fixed star he would appear no larger than one of 
the smaller stars. 

The Sun has three motions, as follows : 

1. A rotation upon his axis once in 25 days, 9^ hours. 

2. A revolution around the center of gravity. This 
movement is very slight. 

3. A revolution around some distant and unknown 
centre, carrying with him the entire solar system at a rate 
of 20,000 miles an hour, and traveling in an orbit so 
great that to make one complete revolution requires 
about eighteen millio?i years I This is perhaps the most 
astounding of all astronomical movements, and the 
question "Whither are we going ?" may well be asked ! 

The Earth. 

The Earth is one of the eight principal planets. She 
ranks fifth in size, and third in her distance from the sun. 
Her distance varies between 91 and 94 million miles. 
She has at least eight distinct motions, but some of them 
it is not our province to consider in this work. Among 
the simpler and better understood of the number are : 

1. Rotation upon her axis every 24 hours. 

2. Revolution around the sun annually in an Elliptical 
orbit. 



42 Lunar Tellurian Manual. 

3. Revolution of the equator around the pole of the 
Ecliptic. (See Precession of the Equinoxes.) 

The Earth's surface is divided into solid and liquid, 
there being about ^ of the former and T V of the latter. 
The solid we call land and the liquid water. The crust 
and liquid covering of the earth as compared with her 
size is :■;■ ;;>/. probably not a hundred miles thick, and 
if shown upon the globe the crust would be reduced to 
the thickness of a thin cardboard ! This crust is sup- 
posed to float on the molten firey interior of the earth. 
Among the proofs that the interior of the earth is a sea 
of fire, are the following : 

1. As we go down into the solid crust of the earth the 
temperature rises at nearly the uniform rate of 1 degree 
for every 50 feet we descend. At a distance of less than 
2 miles, water would boil; at a depth of 10 miles, the 
crust would be red-hot. Below the surface 90 to 100 
miles the temperature would be sufficient to melt any 
substance known to man. 

2. In various parts of the earth's surface we find 
springs of hot water boiling up out of the earth's crust, 
and we know of no way the water could be heated save 
by the internal fires of the earth. 

3. Volcanoes that seem to act as safety valves, through 
which the Furies of the pent up fires find relief in send- 
ing forth fire, gases and lava. The latter is composed 
of well-known substances, such as rock and minerals 
melted to a liquid form. 

4. The form of the earth flattened at the poles and 
bulged out at the equator, shows that the earth in her child- 
hood (if we may be allowed the term,) must have been in 
a soft, pliable state, in which case the earth would neces- 



Lunar Tellurian Manual. 43 

sarily assume the form she now [has. From what we 
know of the interior of the earth it could not have been 
in this soft plastic state except by the action of heat. 
Geological formations show evidences of great heat at 
some former period of the earth's existence. 

The Moon. 

The Moon's Form 9 Size and Physical Condition. 

The moon, like the earth, is very nearly round. Her 
diameter is 2,160 miles, and her volume is about ■£§ the 
size of the earth and only to,o 0V.0T0" times the size of the 
sun. The moon, to us, appears nearly as large as the sun. 
This is because she is about 400 times nearer to us. A 
ball thrown high in the air seems smaller than when 
tossed up but a few feet. Thus we see the apparent size 
of bodies depends largely upon their distance from us. 

The moon, as seen through a telescope, presents a very 
uneven and broken surface, showing very high moun- 
tains, deep valleys, and the craters of immense volcanoes 
now extinct. The clouded or mottled appearance of its 
surface sometimes called > The man in the moon," and 
which many ignorant people think to be land and water, 
is really due to the difference in the reflecting power of 
the various portions of the moon's surface. The higher 
portions of her surface seem to be composed of lighter 
colored material than the lower, and they will therefore 
reflect more light than the darker colored and lower sur- 
face. If examined through a small telescope or field 
glass, we are able to see some spots on the lighter sec- 
tions brighter than the surrounding surface ; these are 
the summits of mountains, the most prominent being 
craters of volcanoes. The most careful observations of 



44 Lunar Tellurian Manual. 

the moon fail to show any atmosphere. There can be no 
water, for the sun's heat during the long lunar days 
(about a month long) would evaporate it and produce a 
cloud-like film around the moon that could be readily 
seen. 

The results of observations upon the physical condi- 
tions of the moon are such that we must conclude that 
it is a cold, lifeless body, the essential elements of life, 
air and water not being found. 

The Moon's Motions. . 

The moon has three positive motions. 

i. A revolution on her axis once in 29^ days. Thus we 
see the lunar day is 29^ times longer than the terrestrial. 
To an observer, on the moon near its equator, the sun 
would rise in the east and set in the west; but the period 
of time between sunrise and sunset would be equal to 
nearly 15 of our terrestrial days, and when the sun had 
set it would not rise for an equal period. How great 
must be the extremes of temperature ! The lunar day 
must be hotter than anything experienced upon the 
earth, while, during the lunar night the temperature must 
fall to a degree unknown save in the polar latitudes of 
our earth. To an observer on the moon the earth would 
look like a huge moon 13 times larger than the moon 
appears to us. It would present the phases of the moon 
as we see them, but on a grander scale. Owing to the 
moon's slow axial rotation the earth would not appear to 
revolve around it, but merely swing back and forth 
through a few degrees. 

2. A revolution around the earth once in 27^ days. 

3. A revolution with the earth around the sun an- 



Lunar Tellurian Manual. 



45 



nually. The result of the last two motions makes the 
actual path of the moon very peculiar. The second 
motion mentioned, of itself, would carry the moon around 
the earth so that its path would be an ellipse; while, 
however, this movement is going on, the last mentioned 
movement (No. 3) is also in operation and is about 30 
times as rapid as the former, (No. 2,) making the actual 
path an irregular curve sometimes outside and sometimes 
inside the earth's orbit, but its path always curves to the 
sun. The moon's orbital velocity is about 2,300 miles per 
hour, while she follows the earth in her great orbital 
journey at the rate of 68,000 miles an hour, over a thou- 
sand miles a second! 

If the earth were at rest in her orbit the 
path of the moon would be similar to cut 
p No. 1, (E the earth, M the moon, and the 
arrows showing the direction of the moon's 
revolution.) Since the earth is not at rest, 
Cut 1. cut No. 1 shows the relative and not the 
true path of the moon. 





Cut 2. 

Let A in cut 2 represent part of the orbit of the earth, 
and E, B, F, will show the true path of the moon from 
her last to her first quarter, or while traveling from O to 
P as shown in cut 1. The moon makes this path because 
she is carried forward with the earth around the sun from 



46 Lunar Tellurian Manual. 

F. to E, while she is revolving around the earth from O 
to P, cut i. If the moon's path from F to E were 
on the line G, H, she would neither curve to nor from the 
sun, but be traveling on a straight line and at right angles 
to him. If this were true, at the point J she would be 
over 400,000 miles from the earth then at I, but as the 
moon's distance is about 240,000 miles, she must be at K 
instead of J. Hence, the moon's path must be on the 
line E, B, F, which is concave to, or curves towards the 
sun. After passing the point E the moon's orbit curves 
sharply in, and in 14 days crosses to the inside of the 
earth's orbit, as we observe it does at the point F. 

The Sidereal and Synodic revolutions of the Moon* 

The moon revolves around the earth in an elliptical 
orbit once in 27^ days; this is called a sidereal revolu- 
tion. Sidereal means Star. 

Ask the pupils to observe that as the moon ball re- 
volves around the globe it is nearer the globe when on 
one side of it than when upon the other. In like manner 
the moon revolves around the earth ; sometimes she ap- 
proaches within 221,000 miles of the earth. Her great- 
est distance is 259,000. She seldom reaches these ex- 
treme limits; her usual variations are about 13,500 miles 
either way from the average, which is about 240,000 miles. 

Ask the pupils to observe the position of the moon 
and some star near it in the heavens ; on the following 
evening the moon will have moved some distance to the 
eastward; continue the observations through several 
evenings, and note the changes of the moon's position 
in the stars. In 27^ days (about) the moon will have 
passed clear around the heavens and will again appear 
near the star where it was first observed. The moon has 



Lunar Tellurian Manual. 47 

now made one sidereal revolution, (one revolution as re- 
gards the stars). If the sun and not a star were taken 
for the base of the observation the time required for the 
moon to revolve around the earth and be brought to its 
former position relative to the sun would be 293^ days, 
about. This is a sy nodical revolution. 

Call the pupil's attention to the fact that the sun appar- 
ently travels from west to east through the heavens, going 
clear around or 360 degrees in a year (about 365 days), and 
of course must travel on an average nearly a degree a 
day. The moon makes a complete revolution through 
the heavens in 27^ days or about 13 degrees daily, and 
in the same direction that the sun apparently travels. 
Let us suppose the sun, the moon and a star to be in 
line on a given day; on the day following, if observed, the 
sun will be seen about 1 degree east of the star, and the 
moon will be seen about 13 degrees east of the star and 
12 degrees east of the sun. The following day the sun 
will be about 2 degrees east of the star, and the moon 
will be about 26 degrees east of the star and 24 degrees 
from the sun. Observe that at this rate the moon will 
be 275/3 days in passing around the earth and again get- 
ting into line with the star, thus completing the sidereal 
revolution. The sun in the mean time has passed to 
about 27 degrees east of the star, and for the moon to 
overtake him will require about 2\ days additional, thus 
completing the synodical revolution in 295^ days. The 
change of the moon depends upon its relation to the sun 
and not to a star, so, from one new moon to another is 
29^ days (about). 

The phases of the Moon. 

The moon shines by reflected sunlight; like the earth, 



48 Lunar Tellurian Manual. 

one-half of her surface is illuminated by the sun, and 
when any part of the light hemisphere is turned towards 
the earth, we see that portion brightly illuminated, and 
the light it gives us we call moonlight. The moon acts 
as a great heavenly mirror reflecting the sun's light after 
he is gone. The bright side of the moon is of course 
always towards the sun. 

The Dark Moon. 

Ask the pupils to notice that when the moon is be- 
tween the earth and sun the light hemisphere of the 
moon must be hid from the earth. Astronomically we 
say the moon and sun are in conjunction ; as ordinarally 
expressed we say it is the " Dark of the Moon " or " No 
Moon." Demonstrate this by the apparatus. 

New Moon. 

Move the globe forward in the orbit until the moon 
has passed two or three inches to the east of the pointer 
L. Ask the pupils to observe that the moon is not 
now between the globe and the arc S, but has passed to 
the eastward, and that now the hemisphere seen from the 
globe has a crescent of light around the western part, and 
that the " Horns of the Moon" or the ends of the 
crescent point eastward. We say the moon is now new* 
and being but little east of the sun, sets soon after him. 
At new moon when the air is clear we can plainly see the 
outline of the dark hemisphere. When the moon is 
situated nearly between the earth and sun as at new 
moon, the bright or illuminated hemisphere of the earth 

*In fact the moon the moment she passes between the earth and 
sun, or reaches conjunction, becomes *' new," though she is not 
usually called new until the crescent is visible. Hereafter in this 
work New Moon means Conjunction. 



Lunar Tellurian Manual. 49 

is towards the moon. Show this upon the apparatus 
mounted as in Cut No. 1. An observer on the moon's dark 
hemisphere would now have, if we may be allowed the 
term, earthlight, in character similar, though in quantity- 
greater than the light we receive from the moon when it 
is full. The sunlight reflected by the earth to the moon 
is in a diminished quantity re-reflected by her to the 
earth, and by this light twice reflected we see dimly the 
moon's dark hemisphere. The reason why the moon's 
crescent is brighter than the dark hemisphere, is because 
the light coming from it is reflected but once, while that 
from the dark hemisphere is reflected twice, the difference 
in brilliancy showing the loss by the second reflection. 
When new moon occurs while the moon is above the 
ecliptic, as shown in cut No. 1, the moon will be above 
as well as east of the sun and her crescent must appear 
lower than when she is below the ecliptic. Thus we have 
what is called the " dry " and " wet " moon. 

First Quarter. 

Move the arm IX. forward until the moon ball has 
passed one-fourth of the way around the globe from the 
arc S. To an observer on the globe the crescent of light 
during this movement will have increased until now one- 
half of the illuminated hemisphere is in view. The 
moon is now one-quarter of the way around the earth 
from the sun and is in quadrature. The moon is now in 
her first quarter. 

Full Moon. 

Move the arm IX. forward until the moon ball has 

passed one-half the way around the globe and call the 

pupil's attention to the fact that an observer upon the 

earth would see the entire illuminated hemisphere of the 

4 



50 Lunar Tellurian Manual. 

moon, and that as she is almost directly opposite the sun 
she must rise at or near sunset. The moon is now in 
opposition with the sun and we have, illustrated, the phase 
of the moon called the Full Moon. 

Last Quarter. 

Move the arm IX. forward until the moon ball has 
passed three-fourths of the way around the globe and ask 
the pupils to observe, as this is done, the illuminated hem- 
isphere of the moon shifts to the eastward so. that when 
it is brought to the three-quarter position only one-half 
of it is visible to an observer upon the globe. The 
moon is again in quadrature with the sun, and presents 
the phase of the moon in her last quarter. 

Old Moon. 

Move the arm IX. until the moon ball is brought about 
Half way between the last quarter and the dark of the 
moon, and observe that a crescent of light may be seen 
around the eastern side of the moon, the horns of the 
crescent pointing to the west. The moon is now " old/' 
from which position she passes to conjunction and the 
dark moon, thus completing the common phases of the 
moon. 

The Orbit of the Moon. 

The orbit of the moon is an ellipse, her least distance 
from the earth is 221,000 miles, while her greatest dis- 
tance is 259,000 miles. She seldom, however, reaches 
these extreme limits, her usual variations from her mean 
distance of 240,000 miles being about 13,500 miles each 
way. The orbit of the moon crosses the orbit of the 
earth at an angle a little greater than 5 degrees. This is 
shown (somewhat exaggerated) by plate E on the globe^, 



Lunar Tellurian Manual. 51 

which carries the moon ball in an inclined orbit above 
and below the ecliptic. The moon's declination is her 
distance north or south of the ecliptic. In cut No. 1 
the moon is shown above the ecliptic in her greatest 
northern declination. In cut No. 2 she is shown below 
the ecliptic in her greatest southern declination. 

The Moon's Nodes. 

The nodes of the moon are the two points where her 
orbit cuts or crosses the ecliptic. The node where the 
moon crosses the ecliptic coming north is called her 
ascending node, and the opposite one the descending 
node. 

The pupils should fix clearly the moon's nodes in their 
minds, as upon this depends the understanding of much 
that is to follow. 

If the sun and moon could leave a thread of li^ht 
to mark their pathway through the heavens (the sun's 
apparent annual path) we would observe these lines 
running very near each other and to cross at oppo- 
site points of the heavens, so that as viewed from the 
earth the path of the sun would sometimes be above, and 
sometimes below the path of the moan, crossing it at 
opposite points — the moon's nodes. These points of 
crossing are not fixed, but are constantly changing, fall- 
ing back to the westward, on the ecliptic or sun's appa- 
rent path about 20 degrees annually. If the nodes were 
stationary, then the time required by the sun to pass 
from one ascending node to another, manifestly, would be 
a year. Because of the moon's nodes revolving back- 
ward on the ecliptic about 20 degrees annually, he will 
approach her nodes about 19 days earlier than he other- 
wise would. Discarding fractions we have: 1 year, 365 



52 Lunar Tellurian Manual. 

days, less 19 days = 346 days the time required by the 
sun to pass from one ascending node to another. As the 
descending node occurs midway between two ascending 
nodes, we have 346 days -5-2 =173 days as the time from 
the ascending to the descending node, and an equal 
period from the descending to the ascending nodes. 

Move the arm IX. until the moon ball is between the 
globe and the arc S, turn the plate E to the right until 
the centre of the moon ball is opposite the pointer L ; the 
sun and moon are now at the node. Note the day of the 
month under the calendar index G. Move the arm IX. 
forward carrying the globe around the arc S to its former 
position and at the same time turn the plate E about y 1 -^ 
the way around in the opposite direction, and observe, the 
sun has, because of this change in the position of the 
moon's orbit, passed the moon's node about 19 days earlier 
than he would have done had the moon's orbit not 
changed position. 

The Zodiacal Belt. 

The Zodiacal Belt is a band in the heavens lying 8 de- 
grees on either side of the ecliptic, in which the sun, 
moon and the principal planets are seen to move. All 
the planets go around the sun in the same general direc- 
tion, from west to east. The orbit of the earth, the ec- 
liptic, is the base, and from it the inclinations of the orbits 
of the several planets are measured. None of the orbits 
of principal planets cross the orbit of the earth at an 
angle greater than 8 degrees and most of them cross at 
an angle considerably less. If all the planets could leave 
behind them a thread of light to mark their pathway 
through the heavens, we would see that within a belt of 
the heavens 16 degrees wide, lying 8 degrees on either 



Lunar Tellurian Manual. 53 

side of the ecliptic, would lie the orbits of all the prin- 
cipal planets, and in this belt they would be seen to move. 
This band or zone of the heavens is called " The Zo- 
diacal Belt." 

The Signs of the Zodiac. 

The ancient astronomers for some reason not now well 
known, divided the Zodiacal Belt into twelve equal parts 
of thirty degrees each, giving to each sign a name, begin- 
ning with the vernal equinox or the equinoctial colure, 
counting thirty degrees east and naming this " sign " 
"Aries ;" to the next thirty degrees east they gave the 
name " Taurus/' so continuing in the order shown upon 
the base of the globe. Thus we see that a " Sign of the 
Zodiac " is a portion of the heavens having a longitude 
or length of 30 degrees and a latitude or breadth of 16 
degrees. 

Passage of the Moon Through the Signs of the 

Zodiac. 

We learned upon the previous page that the moon had 
her revolution in the Zodiacal belt, and as she passes 
clear around the heavens, 360 degrees, in making her 
sidereal revolution, she must in that time have passed 
once through all the Signs of the Zodiac. If the moon 
passes through the 12 signs of the zodiac in 27J/3 days, 
(a sidereal revolution,) she will occupy about 2^ days in 
passing through one sign. 

Rotate the globe upon its axis until the ecliptic marked 
on the globe lies in a horizontal plane. If you were to 
take a large and wide barrel hoop and place it around 
the entire apparatus and hold it in such a position that 
the plane of the ecliptic extended to the hoop it would 
strike the middle of the hoop all the way around it ; the 



54 Lunar Tellurian Manual. 

hoop would then well show the position of the Zodiacal 
belt for the Lunar Tellurian. Or, if the apparatus were 
placed in a large tub, and water were poured in until one- 
half of the globe ball only remained above the water, 
the surface of the water would be the plane of the eclip- 
tic, and that portion of the tub, say 2 inches above 
and 2 inches below that surface would represent 
the Zodiacal belt. If the tub were made of twelve 
wide staves, each stave would represent a " Sign of the 
Zodiac." Let the globe move forward in her orbit, and 
the moon would be seen by an observer upon the globe, 
to pass through these signs upon the staves from west to 
east, as the moon in the heavens actually does pass 
through, or by the Signs of the Zodiac. 

When we say the moon is in Aries, we mean that the 
moon as seen from the earth is in that sign, or more prop- 
erly, between us and that part of the Zodiacal belt called 
the sign Aries. A very instructive and interesting illus- 
tration may be given by placing the Lunar Tellurian upon 
a table and having the pupils, twelve in number, join 
hands around it. Let each one take the name of the sign 
nearest to him on the base of the globe. Move the arm 
IX. forward, and when the moon ball, in passing around 
the globe, comes between the globe and one of the pu- 
pils, let that pupil speak the name of the sign he repre- 
sents; thus, Mary will say, when the moon ball is oppo- 
site her, " Aries ;" in a moment it has passed Mary and is 
opposite John, who calls out, " Taurus, " and the next 
one says, "Gemini," and the next, "Cancer," and so on 
through the twelve signs. Where the pupils join hands 
will mark the divisions of the signs. 

The writer strongly urges the use of the above illus- 
tration, for by it the children, though quite small, will get 



Lunar Tellurian Manual. 55 

a very clear conception of the Zodiacal Belt, the signs of 
the Zodiac and the way the moon passes through these 
signs. 

Passage of the Sun Through the Signs of the Zodiac. 

The sun passes through the signs of the Zodiac in a 
manner very similar to the moon, and the illustrations 
used to show the passage of the moon through the signs 
may be used to equal advantage to show the sun's pas- 
sage. The sun passes through the twelve signs once 
every year and so occupies about one month in passing 
each sign. The pointer G, cut No. 1, shows at all 
seasons of the year the sign and the degree of the sign 
where the sun is situated. Thus, at the vernal equinox 
we see the sun is in the first degree of the sign Aries. 
Move the arm IX. forward to June 21 and observe that 
in the mean time the sun has passed through the signs 
Aries, Taurus and Gemini and has reached the sign 
Cancer. 

Note. — When studying the change of seasons we saw that on 
June 21st the sun reached its greatest northern limit, 23% degrees 
north of the equator, from which position it turned southward 
towards the equator. Thus we see the sun turns south at the mo- 
ment he reaches the sign Cancer. We derive the word " Tropic " 
from the Greek word trepo, which means to turn. The word Cancer 
shows the position of the sun when it turns southward, and from a 
union of these two we get " Tropic of Cancer." The same is true 
of the turning of the sun northward on December 22d, as it reaches 
the sign Capricornus, thereby giving us " Tropic of Capricorn." 

Passage of the Earth Through the Signs of the 

Zodiac. 

The earth is always said to be in the sign directly oppo- 
site the one where the sun is situated. Thus, when the 
sun is in Cancer the earth is said to be in Capricornus, 



56 Lunar Tellurian Manual. 

where it would be seen by an observer upon the sun's 
surface. 

Eclipses. 

An eclipse in general is the cutting off in whole or in 
part the sunlight, as it falls upon the earth or moon. 
All the planets are opaque ; they absorb in part the sun- 
light that falls upon them, and the remainder after ab- 
sorption is reflected back into space. No light passes 
through them. They cast shadows into space, the extent 
of these shadows depending upon the size of the planet 
and its distance from the sun. The larger the planet the 
larger the shadow, and the farther the planet is from the 
sun the farther the shadow will extend into space. To 
illustrate this, draw a circle on the blackboard a foot in 
diameter to represent the sun, mark this circle S ; two 
feet from this circle draw a small circle, say three inches 
in diameter, mark this circle E to represent the earth. 
Draw a straight line from the top of the circle S to the 
top of circle E, continue the line a foot or more beyond 
E ; next, draw a straight line from the bottom of circle S 
to the bottom of circle E, and continue this straight line 
until it crosses the other line ; the distance from where 
these lines cross, to the circle E, represents the distance 
the shadow of the earth would extend. Draw another 
three inch circle say four feet away from circle S, and 
draw similar straight lines from top to top and bottom to 
bottom of the circles, extending them as in the other 
illustration, and ask the pupils to observe, that now the 
distance from the crossing of the lines to the circle E is 
greater than in the first instance when the circles were 
closer together. Thus we see that the nearer a body of 
a given size is to the sun the shorter will be its shadow, 
and the farther it is from the sun the longer will it ex- 



Lunar Tellurian Manual. 57 

tend. Draw a straight line from the centre of circle S. 
through the centre of circle E, and extend it until it 
reaches the crossing of the two lines before mentioned, 
and ask the pupils to observe that the line last drawn 
may represent the ecliptic, and that it divides the shadow, 
into two equal parts, one-half of which is above and one- 
half below it. So the earth into space casts her shadow, 
equal parts of which lie above and below the ecliptic. 
Thus we see : 

(a) That the shadows cast by any planet, great or 
small, must lie in the plane of that planet's orbit. 

(b) That the shadows cast by the planets are in the 
shape of a cone tapering to a point, the base of the cone 
being equal in diameter to the diameter of the planet, 
the distance to the point or frustum of the cone 
depending upon the distance of the planet from the sun. 

(e) That the diameter of the shadow at any point de- 
pends upon the distance of that point from the body 
casting the shadow. 

The cone-shaped shadow of the planet is called its 
umbra, and to an observer situated in the umbra the sun 
is wholly obscured and to him the eclipse is total. Place 
the observer just outside of the umbra and the sun is 
not wholly obscured to him ; his situation is now in pen- 
umbra. To show the penumbra take the figures upon the 
blackboard used to show the umbra, and in addition 
draw a straight line from the bottom of circle S through 
the top of circle E and extend it a foot or two beyond. 
Draw another straight line from the top of circle S 
through the bottom of circle E and extend it as before, 
the space beyond the circle E on either side of the umbra 
and between it and the lines last drawn shows the pen- 



58 Lunar Tellurian Manual. 

umbra. The shadows of all heavenly bodies must have 
umbra and penumbra. 

Umbra means totality, and penumbra, partiality. 

The Dimensions of the Earth [and Moon's Umbra. 

The length of the earth's umbra is about 860,000 
miles, or about 3^ times farther than the moon is from 
the earth. This is the average length : in December and 
January (because then near the sun) the umbra is about 
843,000 miles, while in June and July (when farthest 
away) her umbra is nearly 872,000 miles. The diameter 
of the earth's umbra at the distance of the moon is on 
an average about 6,000 miles, nearly three times the 
moon's diameter. 

The average length of the moon's umbra is 236,000 
miles. It varies, however, from 221,150 to 252,640 miles. 
Observe that the average length of the moons umbra is a 
little less than her average distance from the earth (240,000 
miles). Therefore, if the moon having her average umbra 
pass between the earth and sun at her average distance from 
us the U7?ibra would not reach the earth by nearly 4000 miles. 
The eclipse in this case would be annular and not total. 
(See amnclar eclipses page 61.) 

The greatest possible diameter of the moon's umbra 
as it falls upon the earth is about 175 miles, and this can 
be only when the moon is at her greatest distance from 
the sun and at her least possible distance from the earth. 

Eclipses are known as solar and lunar and as the 
terms indicate, they are of the sun and moon. 

T -r, ,. , \ Partial or 

Lunar Eclipses may be < , 



c. 1 t« 1- u i Partial, total 

Solar Eclipses may be < ' A 

^ J ( or annular. 



Lunar Tellurian Manual. 59 

Lunar Eclipses. 

If the moon revolved around the earth in the plane of 
the ecliptic she would pass through the earth's shadow 
and be eclipsed at every full moon, and would throw her 
own shadow upon the earth at every new moon. Her 
orbit is, however, inclined to the ecliptic, as shown by 
plate E on the globe. That she may pass through the 
earth's shadow and be eclipsed, the moon must, when 
full, be at or near her node, otherwise she will pass above 
or below the earth's shadow. It is not necessary that 
the moon be exactly at her node to strike the earth's 
shadow, for, if within 10^ degrees either before or after 
the node, she will pass into the earth's shadow and be 
wholly or partially eclipsed, according to her nearness 
to or distance from the node when she " fulls." This 
distance, 10^ degrees either way from the node, is called 
the "lunar ecliptic limits." Thus we see, that at either 
node there is a lunar eclipse limit of 21 degrees ; includ- 
ing both nodes, 42 degrees, within which limits all lunar 
eclipses must occur. 

Move the arm IX. of the globe forward, until the moon 
ball is brought to " full," as shown in cut No. 2 ; loosen 
the screw holding plate E, and turn the plate until the 
gear-wheel that drives the moon ball rests upon the 
lower part of the plate, as shown in the cut ; tighten the 
screw, ask the pupils to observe, that now the full moon 
is below the ecliptic (the line J, as marked upon the 
globe), and that the shadow of the earth will pass above 
the moon and no eclipse will occur. 

B3T" // is important that the pupils remember, that while 
the relative sizes of the earth, sun and moon are shown, 
it is impossible to show their relative distances. If we were 
to do this, the globe should be placed about a mile and a half 



60 Lunar Tellurian Manual. 

from the arc S and the moon ball placed about 20 feet from 
the globe, and if placed at these distances, the moon ball must 
be at or very near the globe's ecliptic when full, in order to 
fall within the shadow; a little variation above or below 
would cause the moon ball to miss the globe's shadow alto- 
gether. 

If full moon occurs when the moon is a few degrees 
(say 10 degrees) before she reaches her ascending node, 
she will pass through the lower portion of the earth's 
shadow, thus covering the upper part of the moon's sur- 
face with shadow, giving a partial eclipse of the moon. 
Should full moon occur when the moon is 10 degrees 
past her ascending node, her lower limb or edge would 
be eclipsed by the higher portion of the earth's shadow. 
Revolve the plate E one-half way around, and ask the 
pupils to observe that now the moon ball is above the 
ecliptic J, and that the shadow must fall below it. If full 
moon occurs when the moon is at or very near her node, 
the entire moon will pass through earth's shadow and 
the eclipse will be total. Such an eclipse will occur 
about midnight June n, the present year, 1881. 

Solar Eclipses. 

There are but two celestial objects that can ever come 
between us and the sun of sufficient size to cut off from 
us the solar light. These two are the moon and 
Venus. The passage of the planet Venus across the 
sun's face, is usually called a transit of Venus. The 
last transit of Venus occurred Dec. 9, 1874. The next 
will take place Dec. 6, 1882, after which no transit will 
occur until June 8, 2004. 

There are three classes of solar eclipses, viz., total 
partial, and annular. Let us treat them in their order. 



Lunar Tellurian Manual. 6i 

All eclipses of the sun, caused by the passage of the 
moon between us and the sun, must occur at new moon. 
Now, if new moon occur while she is in the vicinity of 
her node, an eclipse of some kind must occur. If she is 
at or very near her node, she will pass across the sun's 
face centrally, or very nearly so ; and if at this time she 
happens to be near enough to us, her' umbra will reach 
some portion of the earth's surface, and to that region 
the eclipse will be total. On page 57 we learned that 
the greatest possible diameter of the moon's umbra at 
the earth is 175 miles ; the usual region of totality is very 
much less. Thus we see why total eclipses of the sun 
are visible to so small portions of the earth's surface, 
while a lunar eclipse may be seen from any part of an 
entire hemisphere. The duration of solar eclipses is 
very much less than lunar. The length of totality in a 
solar eclipse can not exceed 6 or 7 minutes, and is usually 
very much less, while the moon may remain totally 
eclipsed for nearly two hours. The apparent size of the 
sun and moon are very nearly the same, and it requires 
the entire body of the moon to hide the sun's disc and 
eclipse him wholly; sometimes she is not able to do even 
this, as we shall shortly see. 

If an observer were stationed on the moon during a 
total lunar eclipse, he would, from his position, see a 
total solar eclipse. To him the apparent size of the 
earth and sun would vary greatly, the former appearing 
between thirteen and fourteen times larger than the lat- 
ter. The observer so stationed could not have an 
eclipse of the earth, as the largest shadow his little orb 
could cast upon us would not be half as large as the 
State of Illinois, and to him it would appear like a mere 
speck floating across the face of the earth. 



62 Lunar Tellurian Manual, 

Outside of the field of totality in a solar eclipse the 
eclipse must be partial when it is seen at all. Suppose 
the City of St. Louis to be near the centre of the field 
of totality of a solar eclipse. At the moment of totality 
in St. Louis an observer in St. Paul would see the moon 
as below the sun, and in the passage by, his face would 
obscure only the lower portion of it ; to him the eclipse 
is partial. An observer at New Orleans would see 
the moon, passing rather above, hiding only his upper 
limb or edge, while a person in South America could not 
see the eclipse at all. 

Move the arm IX. forward until the moon ball is 
brought to new moon as in cut No. i. Move the plate E 
until its highest point supports the moon ball, and ask 
the pupils to observe that, now the moon is above the 
ecliptic J, and the shadow of the moon must fall above 
and not upon the earth; were they placed at their proper 
distance (20 feet). Move the plate E until the moon ball 
falls into the plane of the ecliptic, and ask the pupils to 
observe, that the shadow of the moon in this position must 
fall upon the earth. 

On page 57 we find the average length of the moon's 
umbra is 236,000 miles, and her average distance from 
the earth 240,000 miles, so, should the moon pass 
across the sun's face when so situated the umbra would 
not reach the earth by some 4,000 miles. . The apparent 
size of the moon is now smaller than the sun, and she 
would in this position be unable to hide his entire face 
from us, and when passing by his centre a ring or fringe 
of light would be seen all around the moon. An eclipse 
of this kind is called annular. The word annular means 
like a ring or ring shaped, referring to the ring or fringe 
of light seen around the moon. Thus we see that the 



Lunar Tellurian Manual. 63 

moon must be nearer the earth than her average distance, 
or that the sun must be at greater than his average dis- 
tance to make it possible for the moon to hide his entire 
face and produce a total eclipse of the sun. 

Move the arm IX. forward, and ask the pupils to ob- 
serve, that the apparatus shows the moon sometimes 
nearer the earth than at others. ' 

It is not necessary that new moon occur exactly at the 
moon's nodes to give an eclipse of the sun; if within 16 y 2 
degrees of it either way, she will eclipse him. Thus we 
see the "solar ecliptic limit " is 33 degrees at either node 
or, in all, 66 degrees for both nodes, and within this limit 
must all solar eclipses occur. 

Why more Solar than Lunar Eclipses* 

On page 58 we see the moon must be within 10^ de- 
grees (either before or after) of her node at Full Moon 
to enter the earth shadow, consequently her Lunar 
Ecliptic limit is 10% + 10% — 21 degrees at either 
node, or a total of 42 degrees of her orbit wherein lunar 
eclipses may occur. In the last section we see the solar 
ecliptic limit is 33 degrees at either node, or a total of 
66 degrees in which solar eclipses may occur. Then it 
follows that the proportion of solar to lunar eclipses is 
the same as 66 bears to 42 or as 11 to 7. 

Season of JEclipsesJi 

We have already learned (page 51) that the time from 
one node to another is 173 days. If a new moon occurs 
near ascending node and eclipse the sun, in 173 days 
following, full moon will occur near the descending node 
and she will pass into the earth's shadow and be eclipsed. 
The present year 1881, the moon's nodes occur about 



64 Lunar Tellurian Manual. 

June ii, and December i. The following year they will 
occur about 19 days earlier or about May 22, and No- 
vember 11, and so continue from year to year, owing to 
the falling back of th^ moon's nodes. (See page 50.) 

The Solar Ecliptic limit 33 degrees, is equal in time 
to 36 days. So an eclipse of the sun may occur 18 days 
before or 18 days after the moon's node, which, the pres- 
ent 'year extends from May 23 to June 29; while the 
solar ecliptic limit for the opposite node embraces the 
time from November 12 to December 18. 

The Lunar Ecliptic limit 21 degrees, is equal to 23 
days, thus an eclipse of the moon may take place at any 
full moon occurring nj^ days before or after the node. 
Thus the Lunar Ecliptic season is from May 30 to June 
22, and from November 19 to December 12, of the pres- 
ent year 1881. 

The Period of Eclipses. 

By referring to the subject of the moon's nodes (page 
50,) we find the nodes are not fixed, but have a retrograde 
movement on the ecliptic, nearly 20 degrees* every year, 
or at a rate that will carry them clear around the ecliptic 
in about 18 years, 5 months. If we mark carefully the 
position of the nodes on the ecliptic now, and note the 
eclipses that occur for 18 years, 5 months, and record the 
result, and observe the phenomena for a like period fol- 
lowing, we shall find the eclipses for the latter period al- 
most identical with those of the first. Knowing this, the 
astronomers are able to foretell eclipses to the very day 
and hour a hundred years in advance of their occur- 
rence ! These periods are called the Saros or Period of 
Eclipses. 



Lunar Tellurian Manual. 65 

The Precession of the Equinoxes. 

The precession of the equinoxes is due to a gyratory 
movement of the earth's axis revolving the poles of the 
equator around the poles of the ecliptic. As the equa- 
tor or equinoctial and the ecliptic cut each other at an 
angle of 23^ degrees, so must their axes bisect. Upon 
the globe is marked the equator and ecliptic. The poles 
of the equator are the ends of the axis of the globe, and 
the poles of the ecliptic the points where a vertical line 
drawn through the centre of the globe would cut its sur- 
face. This gyratory movement of the earth's axis is very 
slow, requiring about 25,800 years to complete one revo- 
lution. The effect of the movement is to carry the 
equinoctial and solstitial points backward, slowly, around 
the ecliptic from east to west. The value of this move- 
ment annually is 50.1 seconds of arc. The earth's orbit, 
like all circles, is divided into 360 degrees, these degrees 
subdivided into minutes and the minutes into seconds. 
The exact solar year* is the time required by the earth 
to travel 360 degrees of its orbit, less 50.1 seconds, or 
359 , 59/ , 9.9". To illustrate upon the globe the preces- 
sion, or more properly the recession of the equinoxes, 
proceed as follows : 

1. Arrange the globe as shown in cut II, page 8 ; rotate 
the globe upon its axis until the ecliptic upon the globe 
lies in a horizontal plane. 

2. Move the arm O slowly to the left, completing a cir- 
cle around the standard P, and observe that as this is 

*Quite frequently called the Tropical Year. There are generally reckoned 
three years, i. Sidereal Year, as the time [required by the earth to make one 
complete [orbital movement, or 365 days, 6 hours, 9 minutes, 9 seconds. 2. The 
Solar or Tropical Year, as the time required for the sun's vertical ray to pass from 
tropic to tropic and return, or 365 days, 5 hours, 48 minutes, 46 seconds. 3. The 
Civil Year of 365 and 366 days, according as the year is a common or leap year. 

5 



66 Lunar Tellurian Manual. 

done the poles of the equator describe circles around the 
poles of the ecliptic, (the north pole of the ecliptic on 
the globe being where the 90th meridian east crosses the 
arctic circle.) In like manner the poles of the earth de- 
scribe circles around the poles of the ecliptic once every 
25,800 years, as before stated. 

3. Adjust the globe for the calendar; move the globe 
slowly forward in its orbit, and observe that the pointer 
L traces the ecliptic, crossing the equator, giving equi- 
noxes about March 20th and September 23rd. 

4. Move the arm O a part of the way around the stand- 
ard P, as in 2 above, say one-half of an inch ; move it 
forward in its orbit, and observe that the equinoxes do 
not occur at the same points in the orbit as in the former 
instance, but earlier. Repeat the operation, moving 
the arm O little by little, and observe the equinoctial 
points falling back in the orbit as the arm O is moved. 

5. The vernal equinox occurs as the sun enters the 
first degree of the sign Aries of the Zodiac. If these 
signs were fixed as regards the orbit, manifestly the next 
succeeding vernal equinox would occur 50.1 seconds be- 
fore the sign Aries were reached, and so continue to fall 

back in the signs from year to year. The signs, however, 
are shifted to agree with the falling back of the equinoxes ; 
thus the equinoxes will always occur in the same degree 
and sign as now. The signs, however, do not agree with 
the constellations from which they derive their names. 

Equation of Time. 

Sidereal, Solar and Mean Time* 

Time is a measurement of duration. One of the first 
objects of astronomical study was to find a standard for 



Lunar Tellurian Manual. 67 

the measurement of duration. For this purpose the 
apparent diurnal revolution of the sun marked the be- 
ginnings and endings of the standard days ; while this 
did not mark duration into uniform periods of time, it 
was found to be sufficiently accurate for the civil, and 
the crude astronomical uses of the earlier days. The 
sun-dial served to mark the subdivisions of the day ; but 
as the dial was useless in the night time or in cloudy 
weather, a more reliable indicator was sought in mechan- 
ical devices, similar to our clocks and watches. The 
makers of these were sorely perplexed because they 
could not make their machines " agree with the sun " for 
any considerable time ; because of this, we are told, the 
makers suffered persecution, and their machines fell into 
disrepute, and were little used ; and where used at all, 
they merely supplemented the sun-dial, by which they 
were " regulated " from time to time. 

It was soon discovered that the sun days were not of 
uniform length, and that the machines were the better 
time-keepers. The causes of this variation will be ex- 
plained before we leave the subject. 

The Sidereal Day is the period that elapses between 
two successive transits of any fixed star; this period is 
unvarying. The length of the sidereal day is 24 sidereal 
hours, or 23 hours, 56 minutes, 4 seconds of " mean 
time." 

The Solar Day is the period that elapses between two 
successive transits of the sun ; this period varies in 
length, being sometimes more and sometimes less than 24 
mean time hours. Thus it is that the clock and sun do 
not agree. 

The Mean Day or the Mean Solar Day is the aver- 



68 Lunar Tellurian Manual. 

age length of all the solar days of the year, and is of 
course unvarying in length, and is the standard civil day 
which our clocks and watches are made to keep. The 
mean day is 3 minutes 56 seconds longer than the sid- 
eral day. 

The varying lengths of the solar days depend upon 
two causes : 

1. The unequal velocity at which the earth travels in its- 
orbit, 

2. The inclination of the equator to the ecliptic. 

1. To illustrate that the unequal velocity of the 
earth in its orbit is a cause of the existing varia- 
tion of the lengths of the solar days. 

Arrange the globe as shown in cut 2, page 34, and pro- 
ceed as follows : 

Bring the calendar index to the 21st of June; rotate 
the globe upon its axis until the prime meridian is under 
the pointer Z; extend the pointer L until it is within I 1 r 
of an inch of the globe. Move the globe forward in its 
orbit an entire revolution, and observe that the pointer 
L is by this movement carried from west to east across 
the meridians at a rate that will carry it clear around — 
360 degrees — in one year of 365^ days (about), or a 
trifle less than a decree a dav, on the average. This 
distance is equal in time to 3 minutes 56 seconds. 

Rotate the globe upon its axis from west to east, and 
observe that this movement carries the pointer L across 
the meridians from east to west at a rate that will carry it 
clear around in one day ; so it follows that while the daily 
rotation is carrying the sun's vertical ray 36c degrees from 
east to west, the forward movement of the earth in its 






Lunar Tellurian Manual. 69 

orbit is carrying it back nearly a degree (about 59 minutes 
of distance,) from west to east. Therefore, the earth 
must turn more than once upon its axis to complete a 
solar day. This little " more " in a year amounts to 360 
degrees, a revolution. So the truth is apparent that the 
earth must turn 366 times upon its axis to complete 365 
solar days ; or 366 sidereal days are equal to 365 solar 
days. 

If the movement of the earth in her orbit were uniform 
from day to day throughout the year, the variation would be 
uniform, and the solar days would be of equal length. 

As the orbital movement of the earth is not uniform,* 
and the daily revolution is uniform, a variation in the 
lengths of the solar days must follow. 

2. To illustrate that the inclination of the equator to 
the ecliptic is a cause of the existing variation in 
the lengths of the solar days. 

Arrange the globe as shown in cut 2, page 34. Bring 
the calendar index to the 20th of March, rotate the globe 
upon its axis until the ecliptic lies in a horizontal plane. 
Ask the pupils to observe : That the equator and the 
ecliptic are both great circles, and that a degree of one 
is equal to a degree of the other. That the earth rotates 
in the direction of the plane of the equator. The verti- 
cal sun travels on the ecliptic, a, Move the globe for- 
ward in its orbit a few degrees, and observe that this 
movement has carried the pointer L so many degrees 

*The velocity at which a planet travels depends upon its distance from the sun. 
The nearer to the sun the greater is his attraction, and the greater the velocity 
must be to keep the planet from going to him. The orbit of the earth is an ellipse, 
and the sun is situated in one of the foci. In obedience to this law the earth travels 
faster when near perihelion (Dec, Jan., Feb.) than when near aphelion (June. 
July, Aug.) Other things being equal, it follows that the solar days are longer in 
Winter than in Summer. 



70 Lunar Tellurian Manual. 

east and north on the ecliptic, but has not changed its 
longitude to so great an amount as would have been the 
case if all the movement had been directly east, or with 
the rotation, instead of being at an angle to it. Bring the 
calendar index to March 20, rotate the globe until the 
prince meridian is directly under the pointer L ; move 
the globe forward in the orbit until the pointer Z, 
tracing* the ecliptic, is brought to the 10th parallel. Ob- 
serve that the orbit movement has carried the sun east and 
north ; rotate the globe slowly on its axis from west to east, 
and observe this movement carries the pointer L back 
to the prime meridian not on the line of the ecliptic, but 
following the parallel. Thus the orbital movement car- 
ries the sun forward on an angle, and the daily rotation 
brings it back on a straight line, describing two lines of 
a triangle, of which the ecliptic is the hypothenuse, a 
parallel of latitude and the prime meridian being the 
other* two sides. 

Owing to the angling movement about y 1 -^ of the dis- 
placement is lost, thereby shortening the solar day -^ of 
3 minutes 56 seconds (the average displacement), or 
about 20 seconds, b. Move the globe forward to the 
position it occupies about the 1st of June, and observe 
that from this time until about August istthe movement 
of the sun on the ecliptic is nearer in the direction of 
the rotation than in March. Also, that a degree on the 
ecliptic is greater than a degree upon the parallels to 
which the sun is, at this season, vertical, and the daily 
rotation is slower.* Owing to this, about -^2 of this dis- 
placement is gained, thereby lengthening the solar day 
Y2 of 3 minutes 56 seconds, or about 20 seconds. 

*The surface of the earth at the equator travels faster in its diurnal motion 
than the surface at the tropics, being nearly 250 miles farther from the earth's 
axis. 



Lunar Tellurian Manual. 71 

The Tides. 

The Subjoined Explanation of the Mathematics 
of the Tidal Movements is by Prof. E. Colbert, 
the well known Astronomer of the Chicago Tri- 
bune, 

The waters of the ocean are in ceaseless motion, rising 
and falling twice in each lunar day, or about every 25 
hours. The rising of the waters is called the flow or 
flood tide, and the falling of the same the ebb tide. The 
height to which the waters rise through a number of suc- 
ceeding tides is not uniform, as will be explained here- 
after. The greater are called Spring, and the lesser 
Neap tides. The waters act in obedience to that one 
universal law of gravity, which may be expressed as 
follows : 

All bodies attract all other bodies throughout space directly 
in proportion to the quantity of matter they contain, and in- 
versely as the squares of the distances between them. We 
may further add that the force of attraction is exerted in 
the direction of a straight line joining their centers of 

gravity. The subjoined example will explain the appli- 
cation of this law. 

Let two bodies be placed ten feet apart, the weight of 
A to be 2 tons and that of B 1 ton ; their attraction for 
each other is directly as their matter, or as 2 is to 1. 

Let 10 equal the power of attraction of A for B and 5 
equal the power of attraction of B for A. Separate the 
bodies 20 feet; they now attract each other in the same 
ratio, i. e. 2 to 1, but with diminished power. The square 
of the first distance (10 feet) is 10 X 10 = 100. The 
square of the second distance (20 feet) is 20 X 20 = 400. 



72 Lunar Tellurian Manual. 

According to the law above given the attracting power 
of A and B in the two positions is inversely, as ioo is to 
400, or directly, as 400 is to 100, or as 4 to 1 in the respec- 
ive distances of 10 and 20 feet. Thus we see that at 10 
feet the attractive power is four times greater than it is 
at 20 feet If, as stated, the attracting power of A for B 
at 10 feet is 2, at 20 feet it is 2 -f- 4 = f or \, For B at 
10 feet the power is 1, at 20 feet it is 1 -r- 4 = j£. 

The average tide producing influence of the moon as 
compared with that of the sun is nearly as 2 y 2 is to 1 . The 
tides in open ocean do not rise to exceed 5 7/% feet, while 
in the breakers of the tidal wave as it reaches a conti- 
nent the water rises very much higher. In the Bay of 
Fundy, the waters sometimes rise nearly 100 feet. At 
Boston the tide is usually about 14 feet. 

The tides of our oceans are due to the difference be- 
tween the attractive force exerted by the moon and sun ; 
on the earth as a whole, and on the waters at her surface. 
The following explanation of the theory of the tides only 
applies strictly to such parts of the ocean surface as are 
not near to considerable masses of land surface. The 
retardation of the tidal wave in moving through shallow 
water, with the changes in its direction, speed, and vol- 
ume, caused by continents and islands, are matters which 
belong more to physical geography than to astronomy. 
It may be well to note, however, that even in the deep 
waters of the mid Pacific, the tidal wave is retarded by 
the same cause that makes it travel behind the moon 
instead of keeping directly under her; — friction. The 
tide wave that gathers on the eastern side of the Pacific 
Ocean follows about two hours behind the moon, and 
occupies about forty hours in passing round to our At- 
lantic coast ; — less than a circumference of the globe. 



Lunar Tellurian Manual. 



73 



Let M represent the position of the moon ; A D the 
earth, and E its centre. If we take E A, or E D, the 
earth's radius, as unity, then, for the least possible dis- 
tance of the moon ; MA = 55 ; ME = 56 ; and MD = 
57 nearly. 




<=> 



Let m denote the measure of the moon's attractive 
force at the unit of distance ; it equals about 375,800 
feet. Then the disturbing force on the water at A will 
be measured by 



m 



m 



= 4*40 feet. 



(55) 2 (S6) s 
Similarly ; the moon's disturbing force on the water at 
D is measured by : 



m 



m 



= 4*17 feet. 



(S6) 2 (5 7) 3 ' 
We may also calculate that 



2 m 



(56) 



= 4*28 ; which 



is the mean of the above results, and is the mean tide 
due to the moon acting at her least possible distance. 
The calculation gives 0*12 more for the tide under the 
moon, and o'n less for the opposite tide. The differ- 
ences are really much less than this ; owing to the fact 
that the crests of the two tides are at a and d instead of 
on the line A D. In the open ocean they lag about 43 
degrees behind the place of the moon, and its opposite ; 



74 Lunar Tellurian Manual. 

and are still more retarded when they meet with land 
masses. 

The greatest possible distance of the moon from the 
earth's centre is about 64 times the earth's equatorial 
radius. Calculating as before, we have : 

Direct tide = ^— y 2 - ^y 3 ; = 2 '94 feet. 

m m 

Opposite tide = 77~T 2 — 77~T 2 \ = 2 ' 8 ° f ee *. 

2 m 
Mean tide = tr x » ; = 2*87 feet. 

( 6 4) 3 

In this case, as in the other, the tide equals 2 m di- 
vided by the cube of the relative distance from the 
earth's centre ; plus and minus a small quantity. All 
perturbations due to the force of attraction vary in- 
versely as the cube of the relative distance; plus or 
minus a correction which decreases with an increase in 
the relative distance. 

The least and greatest distances of the moon in her 
(average) orbit, are about 57 and 63}^. These corre- 
spond to 4*06 feet, and 2*94 feet, respectively. Half the 
sum of these two is 3*5 feet, which is about the average 
height of crest of the lunar tide wave in the open ocean. 

The sun also causes a tide. Our distance from him 
when in Perihelion is 23,020, and when in Aphelion 
23,805 times the earth's equatorial radius. The value of 
m^ for these assumptions of distance of the Sun, is 
8,900,000,000,000, nearly. The resulting values of the 
solar tide are 1*44 and 1*30 feet; average 1*37 feet. 

The lunar and the solar tides move after the place of 
their respective causes in the heavens, as the earth turns 
round under them. At the times of New and Full Moon 



Lunar Tellurian Manual. 75 

the two forces coincide, and the united tide is equal in 
magnitude to the sum of the two : being (4*06 + 1*44) 
= 5*50 feet, when the earth is nearest to sun and moon ; 
and (2*94 + 1*30) = 4*24 feet, when both are at their 
greatest distance. When the moon is in her first or third 
quarters, the depression caused by the sun coincides 
with the elevation caused by the moon ; and the tide 
varies from (4*06 — 1*30) = 2*76 feet, when the moon is 
in perigee and the earth in aphelion, to (2*94 — 1*44) 
= i'5 feet, when the moon is in apogee and the earth in 
perihelion. 

The crest of each direct tide is theoretically 40 to 
45 degrees or about 2 hours 50 minutes, late on the 
parallel of latitude corresponding to the declination of 
body causing the tide. That is, if the moon be in 20 
degrees north declination, the direct lunar tide will be 
in 20 degrees of north latitude. The crest of the oppo- 
site tide is, similarly, moving in latitude opposite to the 
declination. Let u denote the angular distance of any 
point on the earth's surface from the crest of the lunar 
wave at a given moment; w its angular distance from the 
crest of the solar wave at the same instant ; A^ the 
height of the lunar crest ; and £, the height of the solar 
crest. Then the height of the tide at the designated 
time and place, will equal : 

A. cos. (2 u) + B. cos. (2 w) : 
remembering that the cosine of an angle greater than 
90 degrees and less than 270 degrees, is essentially 
negative. 



INDEX. 

PAGE. 

General Definitions, - 7-15 

Distributions of Light and Heat, - - - 15-22 

Days and Nights: Equal and Unequal, - 22-25 

The Sun's Apparent Path, - 25-26 

Change of Season, ----- 26-28 

Twilights, - - - - - - - 28-22 

The Sun's Declination, - - - - 32 

To find the Latitude and Longitude of Places, - 32-33 

Longitude and Time, - 35—37 
To Find the Difference of Longitude Between Two 

Places, ------ 37-39 

To Find the Time of Sunrise and the Length of 

Twilight, -.:.-- 39 

The Sun, ------- 40-41 

The Earth, - - - - - - 41-43 

The Moon, ------ 43-44 

The Moon's Motions, Phases, etc., - - 44-52 

The Zodiac, Signs of - - - . - 53-56 

Eclipses, Solar and Lunar, - - - 56-65 

Precession of the Equinoxes, - 65-66 

Equation of Time, ----- 66-70 

The Tides. — By Prof, Colbert, - 71-74 

77 



&A 






Vt 



